what is meant by "crossover phenomena"?

It is fashionable jargon, suitable for Humpty-Dumpty:

When I use a word, it means just what I choose it to mean — neither more nor less.

Gluzman and Yukalov describe it as being like a function in an interval where, although the behaviour of the function is qualitatively different in the vicinity of the different boundaries of the interval, the function is continuous and there is no identifiable phase transition point.

"Crossover" is a general term describing a situation when a system can go from being in one phase to being in another phase as a certain parameter is changed.

The best example of a "crossover" phenomenon I can think of is the BEC-BCS crossover which occurs in cold Fermi gases. There one can tune the scattering length $a$ for pairwise interactions to go from being positive to negative. For $a < 0$ bound states can form and we get a BCS state (Bardeen-Cooper-Schrieffer) due to formation of Cooper pairs. As $a$ is tuned to go from being negative to positive the system "crosses over" from being a BCS to a BEC (Bose-Einstein Condensate).