tmmbsl is used in instant messaging programs and emails etc. as an acronym for:
That made me big smile lol.
It is quite a complex "internet-speak" word because it incorporates an already used acronym within as well as using that nested acronym to just express humour rather than its literal meaning.
It is used when a situation is more humourous than to use tmms (that made me smile) but less humourous than lqtm (laughing quietly to myself).
Most widely used alongside an emoticon of a smile with teeth showing.
Another acronym that is part of the new wave of internet acronyms that are more truthful than current ones such as; lol, lmao and rofl.
Dave: ...Then the guy fell off the toilet and onto the poop he was just trying to clean up!
Roy: tmmbsl! :D
Dave: Yeah it is damn funny