means An official document, typically signed by a judge or authority, that authorizes a specific action such as a search, arrest, or payment — or, more loosely, the justification that makes something reasonable.

from From the Old North French 'warant' (a protector or guarantor), itself from a Germanic root tied to the idea of guarding and vouching for something. It shares deep ancestry with 'guarantee' — the two are essentially the same word that walked through different doors, one keeping the hard 'w' of the north, the other softening into the 'gu' of central French. So at its heart a warrant is a promise of backing: something that stands behind your action and says, this is allowed.