I just watched the first episode. I didn't feel lost, really, but I wonder how much I missed--I haven't watched Torchwood at all before, and only a couple Dr. Who episodes (I understand the two series are connected, but I don't know how). Do I need to catch up on them?
Also, has Mekhi Phifer always looked like Tracy Morgan?
Captain Jack was introduced in Doctor Who in "The Empty Child"/"The Doctor Dances" and was a regular companion for several episodes before being put on a busstation at the end of the Eccleston run. He shows up a couple of times after that. He's got quite a bit of backstory to him, but he also functions pretty well without it (although, really, you should probably check out Children of Earth in order to see why Gwen's on the run and Jack's been in space for several years).
I wound up suffering through the first series of Torchwood and skipping the second; if you watch any of it, just to get an idea what TW is (although it's explained pretty well in Miracle Day) you could check out the first episode of series one.