For the most part, contact is simply an 'out type' rating. Basically the opposite of 'velocity' for pitchers. Batters with low contact will strikeout when they make an out more often, batters with a high contact will ground/fly/foul out more often. It does appear to me, based on a moderate amount of research, that it has a small batting average modifier built in, similar to 'pitches' for a pitcher. I would say a batter at the high end of the spectrum will have a batting average 20pts or so higher than one at the low end of the spectrum. Not a huge difference, but it is something.
In considering K-outs vs Ground-outs, the overall effect is pretty similar. Guys who strikeout don't ground into double plays. Guys who ground out, will hit into DPs, but can also reach via the error and move runners over occasionally. I would lean towards a high contact rating for fast players, because they will avoid DPs, and a low contact rating for slow players, because they will be DP machines otherwise.