As Douglas Mayle noted, it basically denotes a type name. Consequently, you would be ill-advised to end variable or function names with ‘_t‘ since it could cause some confusion. As well as size_t, the C89 standard defines wchar_t, off_t, ptrdiff_t, and probably some others I’ve forgotten. The C99 standard defines a lot of extra types, such as uintptr_t, intmax_t, int8_t, uint_least16_t, uint_fast32_t, and so on. These new types are formally defined in <stdint.h> but most often you will use <inttypes.h> which (unusually for standard C headers) includes <stdint.h>. It (<inttypes.h>) also defines macros for use with the printf() and scanf().
As Matt Curtis noted, there is no significance to the compiler in the suffix; it is a human-oriented convention.
However, you should also note that POSIX defines a lot of extra type names ending in ‘_t‘, and reserves the suffix for the implementation. That means that if you are working on POSIX-related systems, defining your own type names with the convention is ill-advised. The system I work on has done it (for more than 20 years); we regularly get tripped up by systems defining types with the same name as we define.