After a breakout, price often pulls back to the broken level. If old resistance now acts as support, the breakout is confirmed. If price falls straight back through, the breakout failed.
Waiting for the retest gives a tighter stop-loss and better risk-reward-ratio at the cost of sometimes missing the trade entirely.
Example: a stock breaks $60 and runs to $63. Two days later it dips to $60.20, holds, and turns up. Entry at $60.50 with a stop at $59.40 risks $1.10 for the move you originally wanted.
Related: breakout, support, resistance, pullback