Can someone explain to me what the mysterious gateA20() calls mean in
   the i386 boot routines?

Welcome to PC Hell.

In order to support braindead PC applications (like some ancient copy
protection schemes) that assume addresses wrap around after 1MB, by
default the `A20 line' (bit 20 on the address bus) is disabled.  The
gateA20() function turns on this bit so that memory above 1MB is
mapped correctly.