The /bin and /usr/bin directories contain public commands. Those commands may be in binary, or in shell format.
Binary format commands are those written in C, FORTRAN, or any other compiler language. The shell format commands are interpreted by the C or Bourne shells, whichever executes them (more on shells later).
When UNIX was first written, /bin and /usr/bin physically resided on two different disks: /bin being on a smaller faster (more expensive) disk, and /usr/bin on a bigger slower disk. This is why /bin contains the more frequently used programs and /usr/bin contains the remainder.