It's a shorthand way of declaring a var. Although "int i = new int()" isn't too much to type, when you start getting to longer types, you end up with a lot of lines that look like:
SomeReallyLong.TypeName.WithNameSpaces.AndEverything myVar = new SomeReallyLong.TypeName.WithNameSpaces.AndEverything();
It eventually occurred to someone that the compiler already knew what type you were declaring thanks to the information you were using to initialize the var, so it wouldn't be too much to ask to just have the compiler do the right thing here.