Unsigned Integers (often called "uints") are just like integers (whole numbers) but have the property that they don't have a + or - sign associated with them. Thus they are always non-negative (zero or positive). We use uint's when we know the value we are counting will always be non-negative. For example, if we are counting the number of players in a game, we could use a uint because there will always be 0 or more players.
Unsigned integers are used when we know that the value that we are storing will always be non-negative (zero or positive).
Note: it is almost always the case that you could use a regular integer variable in place of an unsigned integer. The advantage to using the unsigned version (when you know the values contained will be non-negative) is that sometimes the computer will spot errors for you (the program will "crash" when a negative value is assigned to the variable).
We will talk more about assigning and using uints later in class.