Pure form of MDMA (ecstasy), usually a free powder or in capsules. Oftentimes MDA is sold as molly. Should be white in color (when it's pure) but is more often beige or yellow-brown, and sometimes brown or rarely gray.
Molly does not refer to other MDxx amphetaminese nor the 2C and nBOME analogs (all in the phenethylamine family along with MDMA and meth), and does not stand for molecular (there is a lot of misinformation in these UD entries so I included this for completeness).
Friend: what's her name?
Friend: oh never let her go, she's the best!
"They must have been made by a Molly!"