The term "X:W->R" indicates that X is a random variable over the sample space W. Any actual realization of the variable X is a member of set R (which in this case is the set of real numbers). The notation in the second line is a bit eccentric, and the ':' is more often written as '|', which simply means 'such that.' In other words, read it as 's is an element of W, such that X(s)>2'.
You tend to see this notation a lot when dealing with functions or transformations. The meaning is similar, except that you are not dealing with random variables. In such a case "X:W->R" would read 'The transformation X operates on a member of set W transforming it to a member of set R'
The "image" of a transformation (or random variable) is the same as its range. In other words it is the set of all values that a realization of X may take on.
http://mathworld.wolfram.com/Image.html
