It's still pretty murky. Lebanese news outlets with sources in the Syrian government said right away the plane was shot down in Syrian territory. The Turkish president said in transit that Syria had apologized and both pilots were safe. After the president landed he called a press conference and then couldn't give any specifics, and couldn't confirm his earlier statements, butsaid that a search was on for the pilots. Then he went right into a security meeting.
So this could be nothing, or it could be the expansion of the Syrian conflict into another vietnam (NATO on one side, Russia and Iran on the other).
Conspiracy time! My guess is the F-4 was a Wild Weasel variant doing some kind of electronic warfare, or recon. Possibly in support of NATO troops already on the ground in Syria. Turkey has been VERY careful not to make Syria angry, or provoke them in any way. So the presence of a jet from a northern base (per BBC) in or near Syrian territory is kinda suspicious.