Meaning of surface expressions

Surface expression basically means the form you see. It is the result of applying a rule to some (hypothetical) underlying form of a word (or phrase). So the deep structure would be something like 'dog+plural' and the surface form of that would be 'dogs' or 'I+direct object' and 'me'.

It is largely used in generative contexts and even then only historically since the original deep vs. surface structure distinction has been mostly abandoned. It can be a useful shortcut when talking about the results of rules but few people believe that there is actually any such thing as deep structure.