Yes, libcmt is (one of several) implementations of the C standard library provided with Microsoft's compiler. They provide both "debug" and "release" versions of three basic types of libraries: single-threaded (always statically linked), multi-threaded statically linked, and multi-threaded dynamically linked (though, depending on the compiler version you're using, some of those may not be present).
So, in the name "libcmt", "libc" is the (more or less) traditional name for the C library. The "mt" means "multi-threaded". A "debug" version would have a "d" added to the end, giving "libcmtd".
As far as what functions it includes, the C standard (part 7, if you happen to care) defines a set of functions a conforming (hosted) implementation must supply. Most vendors (including Microsoft) add various other functions themselves (for compatibility, to provide capabilities the standard functions don't address, etc.) In most cases, it will also contain quite a few "internal" functions that are used by the compiler but not normally by the end user.
If you want to get a complete list of the functions in "libcmt" (to use your example) you could open one of the Visual Studio command prompts (under "Visual Studio Tools", normally), switch to the directory where your libraries were installed, and type something like: lib -list libcmt.lib
and it'll generate a (long) list of the names of all the object files in that library. Those don't always correspond directly to the names of the functions, but will generally give an idea. If you want to look at a particular object file, you can use lib -extract
to extract one of those object files, then use `dumpbin /symbols " to find what function(s) is/are in that particular object file.