The year is 2030.
Ted Mosby is 52 years old, still sad and alone, while all his friends are married.
He goes to a strip club, gets wasted, and ends up going with one of the dancers, who happens to be a single mother.
The morning after, as Ted prepares for a walk of shame, he walks out to find he woman's two kids on the couch. They awkwardly ask how this random stranger in their house knows their mom.
Ted, being his socially awkward self, tells these two random children his entire life story, leading up to HOW I MET YOUR MOTHER.
Yeah, but all those "... and then you would have never been born." lines wouldn't make much sense.