What does "var" mean in C#?

It means the data type is derived (implied) from the context.

From http://msdn.microsoft.com/en-us/library/bb383973.aspx

Beginning in Visual C# 3.0, variables that are declared at method scope can have an implicit type var. An implicitly typed local variable is strongly typed just as if you had declared the type yourself, but the compiler determines the type. The following two declarations of i are functionally equivalent:

var i = 10; // implicitly typed
int i = 10; //explicitly typed

var is useful for eliminating keyboard typing and visual noise, e.g.,

MyReallyReallyLongClassName x = new MyReallyReallyLongClassName();

becomes

var x = new MyReallyReallyLongClassName();

but can be overused to the point where readability is sacrificed.

It declares a type based on what is assigned to it in the initialisation.

A simple example is that the code:

var i = 53;

Will examine the type of 53, and essentially rewrite this as:

int i = 53;

Note that while we can have:

long i = 53;

This won't happen with var. Though it can with:

var i = 53l; // i is now a long

Similarly:

var i = null; // not allowed as type can't be inferred.
var j = (string) null; // allowed as the expression (string) null has both type and value.

This can be a minor convenience with complicated types. It is more important with anonymous types:

var i = from x in SomeSource where x.Name.Length > 3 select new {x.ID, x.Name};
foreach(var j in i)
  Console.WriteLine(j.ID.ToString() + ":" + j.Name);

Here there is no other way of defining i and j than using var as there is no name for the types that they hold.