A block confirmation is one unit in the count described under transaction confirmations (TCs), and that entry covers the concept in full. When a transaction is included in a block, it has one confirmation; each further block added on top of it adds another.
Confirmations matter because on proof-of-work chains such as Bitcoin, recent blocks can occasionally be replaced if a competing chain becomes longer. The more blocks built on top of a transaction, the more work an attacker would need to reverse it, so the risk falls with each confirmation. Exchanges and payment processors therefore wait for a set number of block confirmations before crediting deposits, with the number depending on the chain, the amount and their risk appetite. This idea is known as probabilistic finality.
"Block confirmation" stresses that confirmations are counted in blocks, while "transaction confirmation" stresses what is being confirmed; the two are used interchangeably. On some proof-of-stake and other networks with explicit finality rules, a transaction becomes final after a checkpoint rather than a block count, which is a different notion of settlement finality.