"Transfer partners" is one of those phrases that sounds complicated the first time you hear it and is actually a fairly simple idea once someone explains it in plain terms. Here it is, without the jargon.
Some credit card rewards programs let you move your points out of the card's own system and into a different program, usually an airline's frequent flyer program or a hotel's loyalty program. That airline or hotel is called a transfer partner. Once your points land in their program, you book directly with them, the same way anyone else using that airline or hotel loyalty program would.
Why bother moving them at all, instead of just booking through your card's own travel portal? Because the value per point is often different, sometimes significantly, between the two. Your card's own portal usually prices redemptions in a fairly standard, predictable way. A specific airline or hotel program, on the other hand, might price the exact same flight or room for meaningfully fewer points, because their own internal award chart works differently than a generic cash-value conversion. When that gap exists, transferring first and booking direct can stretch the same pile of points noticeably further.
The trade-off is that transfers are usually final, once you move points into an airline or hotel account, they typically cannot be moved back. That is the entire reason to check both options, your card portal's price and the transfer partner's price for the same trip, before deciding. If the portal price is close enough, staying put is simpler and there is nothing wrong with that. If the transfer partner is clearly better, that five extra minutes of checking is where a meaningful amount of value gets captured.
You do not need to memorize every airline and hotel partnership to use this well. You just need to remember the one habit: before redeeming, glance at whether your card offers transfer partners for the trip you are planning, and compare that price to the direct portal option. That single check is most of what "using transfer partners" actually means in practice.