What is a IRepository and what is it used for?

MVC promotes separation of concerns, but that doesn't stop at the M V C level.

Data Access is a concern in itself. It should be done in the M bit of MVC, ie the model. How you structure your model is up to you, but people usually follow tried and tested patterns (why reinvent the wheel?). The Repository Pattern is the current standard. Don't expect a simple formula, however, because the variations are as many as there are developers, almost.

IRepository is just an interface that you create (it is not part of MVC or ASP.NET or .NET). It allows you to "decouple" your repositories from real implementations. Decoupling is good because it means your code...:

1. Your code is much more reusable. This is just plain good.
2. Your code can use Inversion of Control (or Dependency Injection). This is good to keep your concerns well separated. It is especially good because this allows Unit Testing...
3. Your code can be Unit Tested. This is especially good in large projects with complex algorithms. It is good everywhere because it increases your understanding of the technologies you are working with and the domains you are trying to model in software.
4. Your code becomes built around best practices, following a common pattern. This is good because it makes maintenance much easier.

So, having sold you decoupling, the answer to your question is that IRepository is an interface that you create and that you make your Repositories inherit from. It gives you a reliable class hierarchy to work with.

I generally use a generic IRepository:

IRepository

Where TEntity is, well, an entity. The code I use is:

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;

namespace Wingspan.Web.Mvc
{
    public interface IRepository<TEntity> where TEntity : class
    {
        List<TEntity> FetchAll();
        IQueryable<TEntity> Query {get;}
        void Add(TEntity entity);
        void Delete(TEntity entity);
        void Save();
    }
}

A concrete implementation of this interface would be:

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Data.Linq;

using Wingspan.Web.Mvc;

namespace ES.eLearning.Domain
{
    public class SqlRepository<T> : IRepository<T> where T : class
    {
        DataContext db;
        public SqlRepository(DataContext db)
        {
            this.db = db;
        }

        #region IRepository<T> Members

        public IQueryable<T> Query
        {
            get { return db.GetTable<T>(); }
        }

        public List<T> FetchAll()
        {
            return Query.ToList();
        }

        public void Add(T entity)
        {
            db.GetTable<T>().InsertOnSubmit(entity);
        }

        public void Delete(T entity)
        {
            db.GetTable<T>().DeleteOnSubmit(entity);
        }

        public void Save()
        {
            db.SubmitChanges();
        }

        #endregion
    }
}

This allows me to write:

SqlRepository<UserCourse> UserCoursesRepository = new SqlRepository<UserCourse>(db);

Where db is a DataContext instance injected into, say, a Service.

With UserCoursesRepository I can now write methods in my Service class like:

public void DeleteUserCourse(int courseId)
        {
            var uc = (UserCoursesRepository.Query.Where(x => x.IdUser == UserId && x.IdCourse == courseId)).Single();
            UserCoursesRepository.Delete(uc);
            UserCoursesRepository.Save();
        }

And now in my controllers, I can just write:

MyService.DeleteUserCourse(5);
MyService.Save();

With this pattern the development of your app becomes more of an assembly line that leads up to a VERY simple controller. Every piece of the assembly line can be tested independently of everything else, so bugs are nipped in the bud.

If this is a long, unwieldy answer it is because the real answer is:

Buy Steven Sanderson's book Pro ASP.NET MVC 2 Framework and learn to think in MVC.

An IRepository is an interface you specify when you want to implement the Repository Pattern. As @Brian Ball stated, it's not part of .NET it is an interface that you create.

Developers using the Repository Pattern widely recommend the use of an interface for the implementation. For example, in the application I am developing right now, I have 5 repositories. 4 specific and 1 generic. Each one inherits from an IRepository which ensures I will not have issues down the road with differences in implementations.

As far as code examples, I'll try:

interface IRepository<T> where T : class {
    IQueryable<T> Select();
}

Implemented as a generic repository:

public class Repository<T> : IRepository<T> where T : class {
    public IQueryable<T> Select() {
        return this.ObjectContext.CreateObjectSet<T>();
    }
}

Implemented as a specialized repository:

public class EmployeeRepository : IRepository<Employee> {
    public IQueryable<Employee> Select() {
        return this.ObjectContext.Employees;
    }
}

Both the Repository<T> and EmployeeRepository implement IRepository, however they go about performing the querying slightly differently. The generic repository has to create an object set of T before it can try to do anything.

Keep in mind that Repository<T> is supposed to be locked to the interface, where as EmployeeRepository can implement more specialized methods to accomplish more complex logic.

I hope this helps you a little.