This facility is being done by what's called Bash Completion. The files that back this are stored under /etc//etc/bash_completion.d with each command having its own file. So in the git case:

/etc/bash_completion.d/git

If you look at this file you'll notice that it's overloading your environment with extra functions. One in particular is this guy:

$ __git_commands

When you run it you'll get the list of sub-commands.

$ __git_commands | head -5
  add                       merge-recursive
  add--interactive          merge-resolve
  am                        merge-subtree
  annotate                  merge-tree
  apply                     mergetool

Knowing that these are simply functions in your environment you can do this:

$ __git<tab><tab>
__git_aliased_command                __git_complete_remote_or_refspec     __git_diff_index_files               __git_index_files                    __git_refs
__git_aliases                        __git_complete_revlist               __git_diff_index_helper              __gitk_main                          __git_refs2
__git_commands                       __git_complete_revlist_file          __gitdir                             __git_list_all_commands              __git_refs_remotes
__gitcomp                            __git_complete_strategy              __git_find_on_cmdline                __git_list_merge_strategies          __git_remotes
__gitcompadd                         __gitcomp_nl                         __git_func_wrap                      __git_list_porcelain_commands        __git_tags
__gitcomp_file                       __git_compute_all_commands           __git_has_doubledash                 __git_ls_files_helper                __git_wrap__gitk_main
__git_complete                       __git_compute_merge_strategies       __git_heads                          __git_main                           __git_wrap__git_main
__git_complete_diff_index_file       __git_compute_porcelain_commands     __git_index_file_list_filter         __git_match_ctag                     
__git_complete_file                  __git_config_get_set_variables       __git_index_file_list_filter_bash    __git_pretty_aliases                 
__git_complete_index_file            __git_count_arguments                __git_index_file_list_filter_compat  __git_reassemble_comp_words_by_ref   

To get a list of all the Bash Completion functions which give various info about git the command.