To prevent water from getting underneath your backsplash fabricators will caulk that joint using 100% silicone. Since the caulk is flexible, it is able to shift and move with the counters as the house settles over time. Eventually the caulking will discolor or become moldy. At this point it is time to replace the caulk, because its ability to stop water has been compromised.
Another thing to keep in mind is that as the silicone caulking cures it shrinks. So you may notice a gap between your counter and your backsplash a few days after your new counters were installed. Should you notice this on a new installation or on your older counters you see the signs that is time to have your caulking replaced, have the joint re caulked immediately. The cost to re caulk is MUCH less than the cost to replace everything that water, mold and mildew will do to your walls and cabinetry.