First, I want to explain an assumption that I make for this answer. It is not always true, but quite often:

Interfaces are adjectives; classes are nouns.

(Actually, there are interfaces that are nouns as well, but I want to generalize here.)

So, e.g. an interface may be something such as IDisposable, IEnumerable or IPrintable. A class is an actual implementation of one or more of these interfaces: List or Map may both be implementations of IEnumerable.

To get the point: Often your classes depend on each other. E.g. you could have a Database class which accesses your database (hah, surprise! ;-)), but you also want this class to do logging about accessing the database. Suppose you have another class Logger, then Database has a dependency to Logger.

So far, so good.

You can model this dependency inside your Database class with the following line:

var logger = new Logger();

and everything is fine. It is fine up to the day when you realize that you need a bunch of loggers: Sometimes you want to log to the console, sometimes to the file system, sometimes using TCP/IP and a remote logging server, and so on ...

And of course you do NOT want to change all your code (meanwhile you have gazillions of it) and replace all lines

var logger = new Logger();


var logger = new TcpLogger();

First, this is no fun. Second, this is error-prone. Third, this is stupid, repetitive work for a trained monkey. So what do you do?

Obviously it's a quite good idea to introduce an interface ICanLog (or similar) that is implemented by all the various loggers. So step 1 in your code is that you do:

ICanLog logger = new Logger();

Now the type inference doesn't change type any more, you always have one single interface to develop against. The next step is that you do not want to have new Logger() over and over again. So you put the reliability to create new instances to a single, central factory class, and you get code such as:

ICanLog logger = LoggerFactory.Create();

The factory itself decides what kind of logger to create. Your code doesn't care any longer, and if you want to change the type of logger being used, you change it once: Inside the factory.

Now, of course, you can generalize this factory, and make it work for any type:

ICanLog logger = TypeFactory.Create<ICanLog>();

Somewhere this TypeFactory needs configuration data which actual class to instantiate when a specific interface type is requested, so you need a mapping. Of course you can do this mapping inside your code, but then a type change means recompiling. But you could also put this mapping inside an XML file, e.g.. This allows you to change the actually used class even after compile time (!), that means dynamically, without recompiling!

To give you a useful example for this: Think of a software that does not log normally, but when your customer calls and asks for help because he has a problem, all you send to him is an updated XML config file, and now he has logging enabled, and your support can use the log files to help your customer.

And now, when you replace names a little bit, you end up with a simple implementation of a Service Locator, which is one of two patterns for Inversion of Control (since you invert control over who decides what exact class to instantiate).

All in all this reduces dependencies in your code, but now all your code has a dependency to the central, single service locator.

Dependency injection is now the next step in this line: Just get rid of this single dependency to the service locator: Instead of various classes asking the service locator for an implementation for a specific interface, you - once again - revert control over who instantiates what.

With dependency injection, your Database class now has a constructor that requires a parameter of type ICanLog:

public Database(ICanLog logger) { ... }

Now your database always has a logger to use, but it does not know any more where this logger comes from.

And this is where a DI framework comes into play: You configure your mappings once again, and then ask your DI framework to instantiate your application for you. As the Application class requires an ICanPersistData implementation, an instance of Database is injected - but for that it must first create an instance of the kind of logger which is configured for ICanLog. And so on ...

So, to cut a long story short: Dependency injection is one of two ways of how to remove dependencies in your code. It is very useful for configuration changes after compile-time, and it is a great thing for unit testing (as it makes it very easy to inject stubs and / or mocks).

In practice, there are things you can not do without a service locator (e.g., if you do not know in advance how many instances you do need of a specific interface: A DI framework always injects only one instance per parameter, but you can call a service locator inside a loop, of course), hence most often each DI framework also provides a service locator.

But basically, that's it.

P.S.: What I described here is a technique called constructor injection, there is also property injection where not constructor parameters, but properties are being used for defining and resolving dependencies. Think of property injection as an optional dependency, and of constructor injection as mandatory dependencies. But discussion on this is beyond the scope of this question.