a period of deliberate romantic and sexual non-involvement. This may be a time to focus on economic, educational or emotional health.
May be expressed with or without preceding 'a' (either is correct).
total hottie "Hey do you want to go on a date?"
me "You're gorgeous and that's flattering, but I'm on babecation right now. Sorry."
cutie "Can we hook up tonight?"
me "Aww, thank you, but no. I'm on a babecation."