Mere means pure and simple, nothing more and nothing less. If the mere mention of someone's name makes you happy, then just hearing his name — and that alone — is enough to make you smile.
Mere can have a little irony attached. If you introduce yourself as "a mere student," when you’re announcing your astounding invention, you're contrasting your lowly status with the enormity of your invention. This kind of mere comes from the Latin for "undiluted." Mere has a homograph — a completely different word that's spelled the same — and this mere means a lake or a pond. It’s related to the Dutch word meer — there’s lots of water in Holland.