Hello,
I should show that a surjective, continuous map f:X->Y is an identification if it admits a section s:Y->X.
I don't understand the part: "it admits a section s:Y->X." what does this mean?
what is a section?
I believe that a section (see also here) is a right inverse of a given function. That is, $\displaystyle \displaystyle s$ is a section of $\displaystyle \displaystyle f$ is $\displaystyle f \circ s = \mathrm{id}$. Sometimes a section is defined as a function that has a left inverse (so it itself is a right inverse).
Correspondingly, "to admit a section" means to have a right inverse.