A SESQUIANNUAL meeting is one that occurs one and a half times every year; equivalently, 3 times every 2 years, or once every 8 months. It comes from the Latin prefix "sesqui-", which means "one and a half times", and "annual", which means "happening once every year".
This is NOT to be confused with SESQUIENNIAL, which means every one and a half years, or 18 months. A linguist or Latin scholar, the joke suggests, should be able to figure sesquiannual out as "half-and-one every year".
This is an extension of the common confusion between "biannual," meaning "twice a year", and "biennial", meaning "once every two years". Compare with the Sesquicentennial Exposition celebrating the first 1½ centuries of the United States.