There are two switch settings on the furnace hot air plenum that
control this. One sets the temp when the blower turns on, the other
sets the temp when the blower turns off. The turn on is set higher
than the turn off. That way, the first air to come out is nice and
warm. The turn off is lower, so that after the burner shuts off, it
keeps air moving to get just about all the heat out of the furnace.
Sounds like yous are set incorrectly. My furnace will do the on/off
action your describing if the house is very cold, like 40 degrees and
the furnace is turned on. It occurs then because the air is so cold,
that after the blower starts, the cold incoming air drops the air temp
in the hot air penum below the shut off temp. After awhile, as the
temp rises, it starts behaving normally. Under normal conditions, the
burner should come on, then a couple mins later the blower, then after
15 mins or so the burner shuts off, then a few mins later the blower
shuts off, completing the cycle.