The adjective eager describes someone is excited about or impatient for something. If you want to be a doctor one day, you might be eager to dissect a frog in biology. Your squeamish friend? Not so eager.
Eager derives from old words meaning "sharp, pungent or keen," and eager carries that sense of sharpness still. In fact, being overeager is a criticism; someone overeager is likely to make a mistake because they are moving too quickly or not thinking things through before they act.