The easiest way of understanding interfaces is that they allow different objects to expose COMMON functionality. This allows the programmer to write much simplier, shorter code that programs to an interface, then as long as the objects implement that interface it will work.
Database Providers:
There are many different database providers, MySQL, MSSQL, Oracle, etc. However all database objects can DO the same things so you will find many interfaces for database objects. If an object implements IDBConnection then it exposes the methods Open() and Close(). So if I want my program to be database provider agnostic, I program to the interface and not to the specific providers.
IDbConnection connection = GetDatabaseConnectionFromConfig()
connection.Open()
// do stuff
connection.Close()
See by programming to an interface (IDbconnection) I can now SWAP out any data provider in my config but my code stays the exact same. This flexibility can be extremely useful and easy to maintain. The downside to this is that I can only perform 'generic' database operations and may not fully utilize the strength that each particular provider offers so as with everything in programming you have a trade off and you must determine which scenario will benefit you the most.
Collections:
If you notice almost all collections implement this interface called IEnumerable. IEnumerable returns an IEnumerator which has MoveNext(), Current, and Reset(). This allows C# to easily move through your collection. The reason it can do this is since it exposes the IEnumerable interface it KNOWS that the object exposes the methods it needs to go through it. This does two things. 1) foreach loops will now know how to enumerate the collection and 2) you can now apply powerful LINQ exprssions to your collection. Again the reason why interfaces are so useful here is because all collections have something in COMMON, they can be moved through. Each collection may be moved through a different way (linked list vs array) but that is the beauty of interfaces is that the implementation is hidden and irrelevant to the consumer of the interface. MoveNext() gives you the next item in the collection, it doesn't matter HOW it does it. Pretty nice, huh?
Polymorphism
When you are designing your own interfaces you just have to ask yourself one question. What do these things have in common? Once you find all the things that the objects share, you abstract those properties/methods into an interface so that each object can inherit from it. Then you can program against several objects using one interface.
And of course I have to give my favorite C++ polymorphic example, the animals example. All animals share certain characteristics. Lets say they can Move, Speak, and they all have a Name. Since I just identified what all my animals have in common and I can abstract those qualities into the IAnimal interface. Then I create a Bear object, an Owl object, and a Snake object all implementing this interface. The reason why you can store different objects together that implement the same interface is because interfaces represent an IS-A replationship. A bear IS-A animal, an owl IS-A animal, so it makes since that I can collect them all as Animals.
var animals = new IAnimal[] = {new Bear(), new Owl(), new Snake()} // here I can collect different objects in a single collection because they inherit from the same interface
foreach (IAnimal animal in animals)
{
Console.WriteLine(animal.Name)
animal.Speak() // a bear growls, a owl hoots, and a snake hisses
animal.Move() // bear runs, owl flys, snake slithers
}
You can see that even though these animals perform each action in a different way, I can program against them all in one unified model and this is just one of the many benefits of Interfaces.
So again the most important thing with interfaces is what do objects have in common so that you can program against DIFFERENT objects in the SAME way. Saves time, creates more flexible applications, hides complexity/implementation, models real-world objects / situations, among many other benefits.
Hope this helps.