A nonce is a sequential running number of all the transactions ever executed by a given Ethereum address (beginning with 0 for the first transaction). In layman's terms, a nonce is your ticket order, with a lower number nonce being processed before the next transaction (ie, a tx with a nonce of 14 would process before a tx with a nonce of 15).

Fun fact: the word "nonce" comes from cryptography, and is an amalgamation of the words "number" and "once". In other words, a number you can only use once. Cool, huh!?