Is it a reflection of how they feel about their current depth? Is there an injury? Are they interested in adding a fourth layer to the depth chart?
In most cases, but not all, the answer is usually that it's solely for emergency purposes. If the team has an injury or an unexpected trade interest in top backup Ryan Mallett, who enters the final year of his contract, it needs to be ready with a replacement and part of that is having as up-to-date information on the health and skills of available players as possible.
That likely best explains why the Patriots had Quinn in for a workout, as he was previously on the radar as a possible "free-agent fit" based on his experience in the team's system.
With Tom Brady, Mallett and Jimmy Garoppolo, the current quarterback depth chart is well stocked, with Bill Belichick previously saying, "We feel like we have a good quarterback situation. I think there are a lot of teams in the league that maybe don't feel that good about that position, and that’s not a good position to not feel good about. We feel very good about the players we have at that spot."