What is the syntax of an ad-hoc command, and what does each part mean?

ansible host-pattern -m module [-a 'module arguments'] [-i inventory]: which hosts, which module, the module's arguments as a quoted string, and optionally which inventory.

* Each part of an ad-hoc command answers one question: where, what, how, and from which list. *

• host-pattern: a single managed host, a group, or all. It is resolved against the inventory, exactly as with --list-hosts.
• -m module: the module to run on the targets, for example ping, user, command. Modules are small programs that carry out tasks.
• -a 'arguments': the module's options as one quoted string, for example 'name=newbie uid=4000 state=present'. Some modules (like ping) need none.
• -i inventory: a different inventory than the one set in ansible.cfg.

Example: ansible servera.lab.example.com -m user -a 'name=newbie uid=4000 state=present' makes sure user newbie with UID 4000 exists on servera.

If you leave out -m, Ansible uses the command module by default.

Go deeper:

• ansible command reference (official docs) — all options including -m, -a, -i, -b (become).
• Introduction to ad hoc commands (official docs) — worked examples per module.