What is a .a (as libcrypto.a) file?

.a files are static library files. They "contain" one or more .o files, i.e. compiled code. To use them, you (often) need the header (.h) files that correspond to the compiled code, but you do not need the source code (.c, .m) itself.

The .a files are produced with the ar utility, and the linker (ld) that is (usually) invoked by your compiler knows their format and how to extract the relevant pieces of code from the archive and into your executable.