A nonce is a sequential ID number for transactions in a given wallet. You can think of a nonce as somewhat similar to a check number in a bank ledger, with the main difference being that nonces must always occur sequentially without skips.
Each transaction that you sign using your wallet will have an associated nonce. This value is automatically determined and passed along from your wallet when submitting a transaction, but there are some cases where nonces must be manually overridden.
Another important detail is that, if two transactions are signed from the same wallet with the same nonce, only the transaction with the higher fee will be accepted as a valid transaction. This principle, in effect, can be used to override or cancel transactions.