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 means that the type of the local being declared will be inferred by the compiler based upon its first assignment:

// This statement:
var foo = "bar";
// Is equivalent to this statement:
string foo = "bar";

Notably, var does not define a variable to be of a dynamic type. So this is NOT legal:

var foo = "bar";
foo = 1; // Compiler error, the foo variable holds strings, not ints

var has only two uses:

1. It requires less typing to declare variables, especially when declaring a variable as a nested generic type.
2. It must be used when storing a reference to an object of an anonymous type, because the type name cannot be known in advance: var foo = new { Bar = "bar" };

You cannot use var as the type of anything but locals. So you cannot use the keyword var to declare field/property/parameter/return types.

"var" means the compiler will determine the explicit type of the variable, based on usage. For example,

var myVar = new Connection();

would give you a variable of type Connection.