Kanji: 寿 modern simplified Japanese ことぶき kotobuki long life
壽 is the classical kanji
If you look at the classical kanji from the the top, the first part is 士 し shi gentleman, which later became a warrior, the next is 一 いち ichi one with the hook suggesting inclusion, the next part is 工 こう kō work, the next part is 一 いち ichi one, the left part is 口 くち kuchi mouth and the right part is 寸 すん sun a little distance. Altogether it means living and working like a gentleman and as time passes, speaking, while little by little feeding the mouth. It makes a good long life.
Interesting that the kanji 寿司 すし sushi also contain long life. Here it means preserving rice. Sushi is rice with vinegar for preservation, because originally it was left-over rice that was used for the little snack. The reading is strictly speaking 当て字 あてじ ateji phonetic reading.
Anyway, back to the mugs. Here the kanji mean long life!