"The Jason Thing" is a secret that Jenna and Garrett fear The Liars will find out. It is not revealed what it is until "Over My Dead Body," when it becomes clear that Jenna and Garrett slipped Jason a note the night or morning after Alison went missing that said, "I know what you did" leading him to question whether he murdered his own sister while under the influence of alcohol.
For a full year after Alison's death, Jason was unsure if he killed his own sister with Spencer Hasting's Field Hockey stick that was buried in the backyard where Toby found it and was later burned. He vigorously questions Spencer after he hears that she claimed that Ian confessed to killing Alison; such information would vindicate him if it is true, so he is very interested in verifying the claim. However, Spencer's vague answer leaves him wholly unsatisfied. He never told anyone about the note until Aria Montgomery approaches him at Ian's funeral in "The Devil You Know." She is speechless and confused, but promises not to tell anyone. He can finally breathe a sigh of relief that he didn't kill his sister.
Jason explicitly states he is not responsible for Ali's death to Peter Hastings in the Rosewood Police Department in "Over My Dead Body." Garrett eavesdrops on their conversation and later reports to Jenna that Jason has figured out that he is not guilty. It's later revealed in Season 3 that Garrett and Jenna were only attempting to frame Jason because Garrett and Alison tricked Jenna into believing Garrett killed Ali. Jenna was trying to protect Garrett from being caught and Garrett was just going along with it to keep Jenna believing the lie.
Although Jenna and Garrett did not explicitly refer to "The Jason Thing" as such in the midseason finale, it is clear that this is what they meant, as I. Marlene King has revealed in an interview that "You’ll find out what "The Jason Thing" is in the mid-season finale."