Thieving means stealing — the act of taking other people's things. As a noun it is uncountable and quite plain-spoken: 'he was caught thieving', 'there's a lot of thieving round here'. It sounds slightly older and more British than 'stealing', and it carries a whiff of small, repeated, low-level crime — pinching things from shops, from bags, from the kitchen — rather than a planned bank robbery.

The form is also an adjective sitting in front of a noun, and this is where you will meet it most often, because English loves it as an insult: 'a thieving little rat', 'keep your thieving hands off my lunch', 'those thieving politicians'. Notice the anger in all three. Used this way it is not neutral description; it is an accusation, and often an affectionate-rude one between people who know each other.

Because it is the -ing form of the verb 'thieve', it also does ordinary grammar work: 'they went thieving', 'he made a living by thieving'. But 'thieve' itself is rare in modern English — most people say 'steal' — so 'thieving' has drifted into being more common than the verb it came from. That is a nice thing to notice: the child outlived the parent.