Matches are used in Strategy Mode to light rockets. You start off with 10 matches, but you can get more by launching 3 or more rockets at once. When a match falls on a fuse, if you don't collect it within 3 turns, it will fizzle out and disappear.
When there are 3 turns left to collect the match, the flame will be yellow. When there are 2 turns left it will be orange. When there is 1 turn left it will be blue.