To encroach is to overstep your bounds, to take over space or rights that belong to another, like your brother whose mess always encroaches on your side of the room you share.
The verb encroach comes from the Old French word encrochier, meaning “seize, fasten on, catch with a hook.” If people slowly take over what belongs to do, they encroach, like people who encroach on your personal space at a crowded concert, or someone whose questions get more and more personal, which encroaches on your privacy.
