CE stands for Christian Era or Common Era. It's an alternative to AD because when AD or Anno Domini means literally "In the year of our lord". Non Christians don't always like giving the impression that they think Jesus is lord.
BCE means before the Christian Era or before the Common Era. It's an alternative to BC. Again BC means literally, Before Christ or "Before the savior". Non Christians don't always like giving the impression that they think Jesus is the savior.