TM most often means a trademark that is not registered. The HTML character entity for trademark is ™ but in late 2000s, not all web browsers understood it; I used <sup><small>TM</small></sup> which shows up as TM. Nowadays, all major browsers can display the character entity.
TM also stands for Maharishi Mahesh Yogi's Transcendental Meditation. The book Bigger Secrets by William Poundstone exposes all sixteen mantras that TM gives out.
TM stands for "Teaching Machine," the artifacts that attach to Pokemon to give them new abilities. See also HM, Hidden Machine.
If you know of other expansions for TM, /msg me.