In .NET’s dependency injection there are three major lifetimes:

Singleton which creates a single instance throughout the application. It creates the instance for the first time and reuses the same object in the all calls.

Scoped lifetime services are created once per request within the scope. It is equivalent to a singleton in the current scope. For example, in MVC it creates one instance for each HTTP request, but it uses the same instance in the other calls within the same web request.

Transient lifetime services are created each time they are requested. This lifetime works best for lightweight, stateless services.

Here you can find and examples to see the difference:

ASP.NET 5 MVC6 Dependency Injection in 6 Steps (web archive link due to dead link)

Your Dependency Injection ready ASP.NET : ASP.NET 5

And this is the link to the official documentation:

Dependency injection in ASP.NET Core

Which one to use

Transient

• since they are created every time they will use more memory & Resources and can have the negative impact on performance
• use this for the lightweight service with little or no state.

Scoped

• better option when you want to maintain state within a request.

Singleton

• memory leaks in these services will build up over time.
• also memory efficient as they are created once reused everywhere.

Use Singletons where you need to maintain application wide state. Application configuration or parameters, Logging Service, caching of data is some of the examples where you can use singletons.

Injecting service with different lifetimes into another

1. Never inject Scoped & Transient services into Singleton service. ( This effectively converts the transient or scoped service into the singleton.)

2. Never inject Transient services into scoped service ( This converts the transient service into the scoped.)

Transient, scoped and singleton define object creation process in ASP.NET MVC core DI(Dependency Injection) when multiple objects of the same type have to be injected. In case you are new to dependency injection you can see this DI IoC video.

You can see the below controller code in which I have requested two instances of “IDal” in the constructor. Transient, Scoped and Singleton define if the same instance will be injected in “_dal” and “_dal1” or different.

public class CustomerController : Controller
{
    IDal dal = null;

    public CustomerController(IDal _dal,
                              IDal _dal1)
    {
        dal = _dal;
        // DI of MVC core
        // inversion of control
    }
}

Transient: In transient, new object instances will be injected in a single request and response. Below is a snapshot image where I displayed GUID values.

Scoped: In scoped, the same object instance will be injected in a single request and response.

Singleton: In singleton, the same object will be injected across all requests and responses. In this case one global instance of the object will be created.

Below is a simple diagram which explains the above fundamental visually.

The above image was drawn by the SBSS team when I was taking ASP.NET MVC training in Mumbai. A big thanks goes to the SBSS team for creating the above image.

This image illustrates this concept well.
Unfortunately, I could not find the source of this image, but someone made it, he has shown this concept very well in the form of an image.

Update: Image reference : ASP.NET Core Service Lifetimes (Infographic) , Author: @WaqasAnwar

• Singleton is a single instance for the lifetime of the application
  domain.
• Scoped is a single instance for the duration of the scoped
  request, which means per HTTP request in ASP.NET.
• Transient is a single instance per code request.

Normally the code request should be made through a constructor parameter, as in

public MyConsumingClass(IDependency dependency)

I wanted to point out in @akazemis’s answer that “services” in the context of DI does not imply RESTful services; services are implementations of dependencies that provide functionality.

AddSingleton()

AddSingleton() creates a single instance of the service when it is first requested and reuses that same instance in all the places where that service is needed.

AddScoped()

In a scoped service, with every HTTP request, we get a new instance. However, within the same HTTP request, if the service is required in multiple places, like in the view and in the controller, then the same instance is provided for the entire scope of that HTTP request. But every new HTTP request will get a new instance of the service.

AddTransient()

With a transient service, a new instance is provided every time a service instance is requested whether it is in the scope of the same HTTP request or across different HTTP requests.

After looking for an answer for this question I found a brilliant explanation with an example that I would like to share with you.

You can watch a video that demonstrate the differences HERE

In this example we have this given code:

public interface IEmployeeRepository
{
    IEnumerable<Employee> GetAllEmployees();
    Employee Add(Employee employee);
}

public class Employee
{
    public int Id { get; set; }
    public string Name { get; set; }
}

public class MockEmployeeRepository : IEmployeeRepository
{
    private List<Employee> _employeeList;

    public MockEmployeeRepository()
    {
        _employeeList = new List<Employee>()
    {
        new Employee() { Id = 1, Name = "Mary" },
        new Employee() { Id = 2, Name = "John" },
        new Employee() { Id = 3, Name = "Sam" },
    };
    }

    public Employee Add(Employee employee)
    {
        employee.Id = _employeeList.Max(e => e.Id) + 1;
        _employeeList.Add(employee);
        return employee;
    }

    public IEnumerable<Employee> GetAllEmployees()
    {
        return _employeeList;
    }
}

HomeController

public class HomeController : Controller
{
    private IEmployeeRepository _employeeRepository;

    public HomeController(IEmployeeRepository employeeRepository)
    {
        _employeeRepository = employeeRepository;
    }

    [HttpGet]
    public ViewResult Create()
    {
        return View();
    }

    [HttpPost]
    public IActionResult Create(Employee employee)
    {
        if (ModelState.IsValid)
        {
            Employee newEmployee = _employeeRepository.Add(employee);
        }

        return View();
    }
}

Create View

@model Employee
@inject IEmployeeRepository empRepository

<form asp-controller="home" asp-action="create" method="post">
    <div>
        <label asp-for="Name"></label>
        <div>
            <input asp-for="Name">
        </div>
    </div>

    <div>
        <button type="submit">Create</button>
    </div>

    <div>
        Total Employees Count = @empRepository.GetAllEmployees().Count().ToString()
    </div>
</form>

Startup.cs

public void ConfigureServices(IServiceCollection services)
{
    services.AddMvc();
    services.AddSingleton<IEmployeeRepository, MockEmployeeRepository>();
}

Copy-paste this code and press on the create button in the view and switch between
AddSingleton , AddScoped and AddTransient you will get each time a different result that will might help you understand this.

AddSingleton() – As the name implies, AddSingleton() method creates a
Singleton service. A Singleton service is created when it is first
requested. This same instance is then used by all the subsequent
requests. So in general, a Singleton service is created only one time
per application and that single instance is used throughout the
application life time.

AddTransient() – This method creates a Transient service. A new
instance of a Transient service is created each time it is requested.

AddScoped() – This method creates a Scoped service. A new instance of
a Scoped service is created once per request within the scope. For
example, in a web application it creates 1 instance per each http
request but uses the same instance in the other calls within that same
web request.

• Transient: A new instance is provided every time an
  the instance is requested whether it is in the scope of same http request
  or across different http requests.

• Scoped: We get the same instance within the scope of a
  given http request but a new instance across different http requests.

• Singleton: There is only a single instance. An instance
  is created, when service is first requested and that single instance
  single instance will be used by all subsequent http request
  throughout the application.