1. When you have every intention of meeting "that" guy for a drink...but don't want him to asume it.
"Ok, I may show up accidentally on purpose"
2. Deliberately, but feigning (not by) accident.
The first printed record of this phrase is from The history of the famous preacher Friar Gerund de Campazas, by José Francisco de Isla, 1772:
Tell us what is Modesty of Voice, for you happened accidentally on purpose to drop this word, and I don't rightly know what it signifies.
Accidentally on Purpose was an American television situation comedy series, which premiered on CBS on September 21, 2009 and concluded on April 21, 2010.