You are right that it is amazingly poorly documented. What documentation that there is is quite simple:
-t Exit after reading and executing one command.
The bash source code is available here. I looked at version 4.2. The short flags handled by bash are listed in flags.c and in there is the relevant line:
{ 't', &just_one_command },
So, -t on the command line sets the variable just_one_command. This variable is used in just one place: it occurs in an if condition at the end of a loop in eval.c:
if (just_one_command)
EOF_Reached = EOF;
In other words, if the -t flag is given, then, after the first command is executed, the end-of-file condition is signaled and bash exits.
MORE DETAIL
From eval.c, command line execution in bash appears to be controlled by the function reader_loop:
reader_loop ()
{
int our_indirection_level;
COMMAND * volatile current_command;
USE_VAR(current_command);
current_command = (COMMAND *)NULL;
our_indirection_level = ++indirection_level;
while (EOF_Reached == 0)
{
int code;
code = setjmp_nosigs (top_level);
[ ... Much code removed ... ]
if (just_one_command)
EOF_Reached = EOF;
}
indirection_level--;
return (last_command_exit_value);
}
The loop inside reader_loop continues until it receives the signal EOF_Reached. The sole effect of the -t option is to set this flag at the end of loop which assures that the loop is executed only once.
bash --helpactually tells you to usehelp setto see descriptions for short options.