It's a platform where people can make simple programs and allow others to use them. Stands for If This Then That, which is the typical programming sequence. Some of the programs are built to take tweets and automatically post them on another platform. That is especially useful when trying to get tweets via SMS. (There is no program on IFTTT that will send tweets to SMS directly. But it can send them to Group Me or Email, which can then be forwarded to SMS.)
You beat me to it!
Basically if there's a sentence "if this then that", you get to make your own sentence, choosing what to fill in for the 'this' and the 'that'. Your choices are a bunch of different triggers from tons of different apps, and a bunch of different actions from tons of apps.
There are tons of examples you can search through here:
https://ifttt.com/discover?source=get_more_header_buttonIt looks like they do offer an SMS service and one called Android SMS:
https://ifttt.com/search/query/sms?tab=services. Anyone want to try them out and see how they work? It seems the android one requires a smartphone, and I didn't see a way to use the regular SMS one as an action. Maybe it's only a trigger?