\\(g\\) is an element of \\(X^B\\), i.e., it is a function from \\(B\\) to \\(X\\). \\(\lambda\\) is the lambda operator from the [Lambda Calculus](https://en.wikipedia.org/wiki/Lambda_calculus) (which I know almost nothing about). So, 2), in words, says that \\(f\\) maps to composition with \\(f\\).

Edit: Maybe there is some way to look at composition with \\(f\\) as what you were describing?