Roughly every 10 minutes, a new "block" is created. If Joe sends Sue a satoshi, it will be at least 9 minutes and 59 seconds until they get 1 confirmation (as I understand it). Then, subsequent blocks will increase the number of confirmations in perpetuity, with 6 blocks equating to roughly one hour.
But up until today, I always thought that "confirmations" were simply fullnodes (such as the non-pruned Bitcoin Core I'm running) "confirming" that the transaction took place.
Is this entirely false? If so, what is the point of my fullnode? Does it have any say/power whatsoever? It seems like the miners are the only ones who matter.