what does it mean to "sweat" the onion and garlic in the ketchup recipe?

More of a melting process where the onions and garlic soften without getting color which would change there character/flavor you are extacting the flavors and oils into the surrounding fat to serve as a base for addditional ingredients.

Also cover the pan with a lid, slightly askew...so it just kinda 'smiles' at you. The steam will help keep them from browning...and as mentioned very low heat.

Basically, you want the onions and garlic to just start to release their liquid until the soften. They shouldn't begin to color- they just need to "sweat" their water. This should be done over a low/medium low heat.

saute over very low flame, slowly, so they don't brown.