The acronym "HMU" in texting stands for "hit me up." It is an acronym that extends the invitation for the receiver to continue conversing with the sender.
Acronyms were created in early text message history to shorten messages due to character or word limits, to simplify texting in general, and to speed up the process of sending a text message. The popularity of using acronyms in text messages was instant and still remains.
Other popular acronyms used in text messages as of 2014 include "IDK," meaning "I don't know;" "IDC," meaning "I don't care;" "LOL," meaning "laugh out loud" and "TTYL," meaning "talk to you later."