By indicates when vaguely something happens, with little precision. In your example it means around the year 2013.
For locations, by means near or next to, it's the same meaning for referring to time instead of space.
For a future date it can also means beforeat some unspecified time before:
The company vowed to ban all plastic containers by 2022.
Renewables can reduce CO2 emissions by 70% by 2050
It's a little weird to use if for a past date but I guess it works to. It would mean at some time before 2013.
I'm not 100% sure about this, but it could also mean around the year 2013.
After all, by is used in that sense for for spacial indications (the first definition is near or next to), so it could also apply for time indications.
He liked to sit by the tree.
It makes sense in your example.