To catch fire is to start burning. Dry grass in August, a tea towel too near the ring, and then it is happening very fast.
No article — catching a fire is not English. Catch has the sense of taking something up, the same as in catch a cold. The second use is the one worth learning: a song, a protest or a phrase catches fire when it suddenly spreads, and English keeps a whole shelf of related images for it, from spread like wildfire to a spark and a flashpoint.
1phrasecatch fireTo start burning.
“Dry grass can catch fire in a matter of minutes.”
2phrasebecomeTo become suddenly and widely popular.
“The song did not catch fire until a film used it.”
Practised in Common Word Pairs