A spark arrestor on an engine is basically a type of metal filter or screen that prevents sparks from a combustion engine from leaving the exhaust and potentially catching something on fire such as dry grass, dry leaves etc.
Without a spark arrestor the engine can sometimes throw out tiny sparks that you may not even notice and as a result could catch dry grass, leaves, brush etc on fire.
A spark arrestor can sometime be located inside the muffler or on the tail pipe end of the exhaust on some engines.
Here's an image of a spark arrestor on a small engine.
