Spoiler ahead for beginners:
I've completed season 2. By the end of season 2 we came to know that Jason is Alec's son. Alec sent him from 2077 to the past(1992 or 1990). We saw in season 1 that he tried to build a time machine to go back to future, he also agreed to take Keira with him. Later that didn't work out as they expected and no mention of his time machine in further episodes.
Then we saw in season 2 that he tried to help Alec in different situations. He tried to help making a program using the Arc for surveillance over anyone. That's also destroyed later by Emily with the permission of Alec after there was a chaos that Lucas did by hacking the program.
We sometimes saw Jason in random scenes, basically doing nothing. In future he was shown as if he has a motive, and in 2013 version, he was shown as if he didn't know what he was doing. Sometimes the impression was given that he lost full control over his mind. He wanted to go back in future as we've seen in the season 1 finale.
In short Alec does everything, Jason tried to help. But series didn't explain by the end of season 2, how Jason is helping Alec to shape the future or with what purpose.
So what is Jason's purpose for which he was sent to the past? Am I missing something?