Only german elites upgrade and they only upgrade when the new technology is gained, so if you have elite warriors and research Iron Working, they become legions. This is a one-time deal. If your non-elite warriors later become elite, they won't upgrade. Also, if you skip a tech, they won't ever upgrade. So if you don't research Iron Working but go straight up to Feudalism, your warriors won't become knights.
The only other way to upgrade is to build Leonardo's Workshop, which works just like the German ability. All your units upgrade at once, but again if there are gaps in your tech, they won't upgrade.
Backfilling gives you free techs provided somebody else already has it researched and you are currently completing a tech at more beakers than the tech you'll get for free's cost. Example: You haven't researched Pottery yet, but France is in the game (starts with Pottery). You are currently making 25 beakers per turn and you complete Ceremonial Burial. You get Pottery for free. If you also lacked Bronze Working and somebody had it, you'd get that too. It's possible to get a big pile of techs for free by setting all your cities to gold and just expanding for a while, then flipping back to tech for a big backfill, but of course you won't get any first to research bonuses.
