The short answer
Usually a dirty flame sensor or a clogged filter.
A furnace that starts, runs a minute and shuts off is usually telling you one of two things.
Check the filter first
A clogged filter overheats the furnace and it shuts itself off to protect itself.
Then the flame sensor
- It is a small rod near the burner.
- Dirt on it makes the furnace think the flame went out.