Plumb means perfectly vertical. A plumb post stands at exactly 90 degrees to a level horizontal datum. The traditional check is a plumb bob (a weighted line that hangs straight down) or a spirit level held against the post face.
For gate work, post plumb matters because the hinge centres on a swing-gate post must be exactly vertical for the gate to swing without binding or sagging. A post that's even 5 mm out of plumb over a 2 m height will pull a 3 m wide gate's leading edge several centimetres out of line over a year.
The install rule: brace each post in concrete with timber struts in two directions until the concrete sets. Check plumb after the brace, before the brace, before the next post, after the gate hangs. Plumb is the single most-checked dimension on any gate install.