In texting lingo, the abbreviation "HMU" stands for "hit me up." This means the sender wants the recipient to contact him in regard to something either by text or phone.
"HMU" generally is used to indicate the sender's desire to get together with the recipient at a later date if he wants to do so. A proper response to "HMU" is for the recipient to tell the sender if he is interested in getting together or not. Ignoring such an invitation is seen as rude in most social circles. It is acceptable to make contact on the day in question as this is seen as "hitting the person up."