What does 'half life' of a protein mean?
"Half-life time" is a general term. This is a time after which the amount of substance X decreases by 50%.

If you take a bulk of something (say, 100 protein molecules), if this protein has half-life time of 1 hr, then 1 hr later you'll have 50 molecules left.

In cellular biology it usually means that 50% of protein got recycled/degraded in given half-life time