In an uptrend, a break of structure is a close above the prior swing-high. In a downtrend it is a close below the prior swing-low. It is a continuation event: the trend just proved itself again.
Traders use it as a filter. If you only take long setups after a bullish break of structure, you are refusing to guess at bottoms and instead waiting for the market to show a direction. The cost is that you enter later and give up the first part of every move.
The term comes from the market-structure school of price action and is often confused with change-of-character, which is the opposite: a break against the trend. Keeping the two straight matters, because one means keep going and the other means be careful.
Related: change-of-character, market-structure, swing-high, swing-low, displacement