For the User:
Contact impacts PCI placement (on any no-control-of-PCI interface - Directional and I think Analog). Higher = more consistently accurate PCI placement.
Contact impacts the expression of PVIS and DISC. You'll check swing easier (DISC) and make more raw contact (PVIS) on higher Contact. Vice versa, of course, for lower.
For the CPU:
It impacts the CPU hitters' strike zone judgement. High Contact can make them chase less (DISC) and make more contact on any swing (PVIS), and increases the size of the PCI.
If the CPU "uses" Directional interface (i.e. that's what's emulated when the CPU hitter places his PCI), then the same effect as above applies - more accurate PCI placement. If it "uses" Zone-type emulation, then it will do the same as for Zone users - larger PCI and "regions" within the PCI.
For Both:
The better PCI location and increased size can increase offense (sometimes dramatically). It impacts the expression Power and Solid Hits (those sliders still work off contact quality, which Contact slider impacts via PCI changes).
Of course, more contact leads to more expressions of power and solid hits (as well as power ratings). It doesn't, on it's own, create more power or better trajectories, per se. It helps creates better bat-ball contact, which increases the odds of better contact quality, which increases the amount of batted ball "oomph" that swing gets.
If you want more "maximum oomph" and carry, you'll need to raise power slider. If you're getting a lot of contact...but it's mostly poor trajectory and "Weak" contact even on good swings, you'll probably need to tweak solid hits.
It works with Timing to set the "forgiveness" of timing errors. The window widens and mistakes cost less. You're more likely to still get decent or better contact on early/late swings. Very early/late are still tough, but you might get fouls instead of misses (or you might get popups as well...bad swings are still bad swings, but instead of whiffs, you might get bloops, flares, choppers, instead).
It works with Foul Frequency in the sense that the "gray area" around the timing window/PCI is expanded because the window/PCI itself is expanded. This can create more contact at more extreme errors - which can create more contact as well (and potentially, more hits).
Contact is a powerful slider a lot of times, but it does have its limits and can only do so much but for raising or decreasing offense. It's like the size of a dart board - you make it small, but if you get a bullseye, you still got a bullseye. Lower contact won't change that and higher won't make a bad throw a bullseye, but you might land on the board at least.