libc is the C library; basically, it contains all of the system functions that most (if not all) programs need to run on Linux. It's similar to a combination of dos.library and exec.library on Amigas, but it also contains a lot of things that are in the C runtime library (like, for example, ixemul.library or the .lib files included with SAS/C and other compilers for AmigaOS).
libc6 and glibc are the same version of libc; officially, it's version 2 of the GNU C Library (but it's the sixth major version of the Linux C library). You can read more about glibc at the GNU C Library pages.
The major versions of libc for Linux/m68k are:
libc4: Version 4 of the C library is based on the a.out binary format; it was the first version to support dynamic linking (shared libraries). However, a.out dynamic linking had a lot of problems (for example, you had to build the library twice, so you could add a jump table to the library on the second pass, and the library was non-relocatable, so every library had to be allocated a block of space to load into), so it was abandoned (at least on m68k; Intel users may still need it for some esoteric applications). You should not be using libc4 for anything any more. If you do use it, we will hunt you down and execute you as an example to others. (Not really, but you get the point...)
libc5: Version 5 of the C library was a fairly big improvement over version 4. However, it still had some problems (adding new functions or changing structure sizes introduced subtle bugs) so it is no longer being actively developed. It was the first version of the Linux C Library based on ELF, a different file format that made programs loadable in more flexible ways (it uses hunks, similar to the AmigaOS executable file format). libc5 is officially deprecated on m68k; use libc6 for new compilations.
libc6: Version 6 of the Linux C Library is version 2 of the GNU C Library; the confusion is because Linux has had multiple C library versions. This is the newest technology available, and includes features (like "weak symbols") that theoretically allow new functions and modified structures in the library without breaking existing code that uses version 6, and avoid kernel version dependency problems. You should be coding and compiling all code against this version.