The word membrane hails from the Latin term membrana, which carried multiple meanings (including “membrane”, “skin”, and “parchment”). This is a conjugated form of the word membrum, which meant “limb” but literally carried the meaning of “a member of your body” (the word member is still used in this context in English, though not so much anymore) as well as being a euphemism for “male sex organ” (another slightly archaic though still used term). We actually got all these English terms from that word, through French membre, and the meaning “person in a group” after the body part definitions because it followed the concept of a part representing a whole. Anyway, the Latin word membrum most likely comes from the reconstructed Proto-Indo-European term mems, which meant "flesh" (though earlier on it may have meant something more like "meat". You can remember it this way: for any group, its members' members are made of meat.
Adam Aleksic, a rising sophomore studying linguistics and government at Harvard University, has been described as the internet's sixth most famous etymologist. He also has disturbing interests in politics, vexillology, geography, board games, conlanging, and law.