A terminal app is the way of providing a command prompt to Android devices.
As Android is based on a Linux kernel, using a terminal allows the user to execute Linux shell commands. Though the command set is restricted (compared with a full fledged Linux desktop installation), it follows the same rules, and commands are mostly compatible to their "pure Linux" equivalents. This also means you can consult Linux man pages concerning their syntax (consult the linked Wikipedia article for further details not only on man pages, but also for a list of Unix utilities, to get an idea what you can do using a terminal app).
