If you suck something, you hold it in your mouth and pull at it with the muscles in your cheeks and tongue, for example in order to get liquid out of it.
sucking-pig
a pig that is not yet weaned
sucking louse
any insect of the order Anoplura
wind-sucking
a harmful habit of horses in which the animal arches its neck and swallows a gulp of air
sucking diesel
doing very well ; successful
suck in
to attract by using an inexorable force, inducement , etc
suck up
You say that someone is sucking up to a person in authority when you do not like the fact that they are trying to please the person because of the person's position.