It rewards two behaviours — improving the price, and committing early. Because the rule is mechanical, a resting order's place in line is knowable, and strategies are built entirely around holding good spots.
Most equity venues and many futures markets use it. The main alternative is pro-rata-allocation, which rewards size instead of speed.
Example: 10,000 shares are bid at 30.00 across four orders that arrived in this sequence: A 2,000, B 5,000, C 1,000, D 2,000. A seller hits 6,000 shares. A fills 2,000, B fills 4,000, and C and D get nothing. If D had bid 30.01 instead, D would have filled first despite being last in time, because price beats time.
Related: queue-position, pro-rata-allocation, matching-engine, order-book