Snatch is a carry-over from SR2 in which you'll driving around rescuing Hos from the Morninstar or Kinzie's contacts from the Deckers - Easy, Medium and Hard difficulties where the number of Snatch targets and the rival gang response get higher based on the level. The activity markers will not show up until Act 2 (your first mission for Zimos is the first level of Snatch) so this is obviously something you can't jump into straight away.
This goes for Tune In, Drop Out as well: I cannot reccommend highly enough upgrading a car before you start!
Grab a fast four-door (Blade or Infuego for me) and make sure you at least give it level four Tire Durability and Frame Durability. Anything else is optional at this stage. That should set you back about $10K (TBC).
Then all you have to do is drive to the Snatch marker and make sure you jump into the set of wheels you prepared earlier.
When you get to each group of targets, take out the gang guards and then recruit the targets (as if they were gang members). Once in your car, drive them back to the start position as fast as possible, ignoring the gangers chasing you - they can't hurt you easily, remember - and repeat as often as required.
As an alternative ride, if you can get your hands on a Bear (the APC) you're pretty much unstoppable - brute force over speed and agility :)