I have the MSI gaming app and I would like to know what OC gaming and silent mode do.

Solution
Is this for a graphics card? If so each mode sets different clock speeds and maybe different fan profiles.
OC mode is for the highest clocks, silent mode will be lower clocks with gaming mode somewhere in the middle.
The OC mode will simply increase the card's clocks a bit higher for slightly better performance, at the expense of more power draw and heat under load, which will require the card's fans to run at a higher speed, making them more audible. Most likely, the additional performance won't be very noticeable, and probably won't amount to much more than a couple FPS in game, but you can test the different modes in some game benchmarks to see how the different profiles affect the performance and noise level of your particular card.