If you want to dig into the phrase, a jot is a small mark - specifically, a small Greek I: the iota. This is considered a very small and insignificant amount. You'll also find phrases like ''I care not one iota!'' (ie. I cannot care even the tiniest amount.)
A tittle is literally the dot on an i.
So ''not one jot or tittle'' can be literally understood as ''not the tiniest amout (such as a small ı), nor even the dot on top''. I'd also understand the phrase as slightly poetic or oratory - the speaker is showing off his/her skill with words.
You'll often see related words paired up in set English phrases: peace and quiet, jot or tittle, goods and chattels, tooth and nail... and so on...