A node is a computer running Bitcoin software that checks every transaction against the rules. Running your own means you don't have to trust anyone else about your balance or the rules.
Go deeperA full node downloads and verifies the entire blockchain, which takes several hundred gigabytes (less in pruned mode). Many people run one on a small dedicated box at home. It's not required to use Bitcoin, but it's the most private and trust-free way to do it.