Soundcheck is a patching preset, retrievable with one button.
What it’s most commonly used for is to patch recorded tracks back through the same tracks they were recorded from in a live recording. So, with Soundcheck off, you could have five live tracks coming into channels 1-5. You hit record MTK and capture them into five files on disk. Then you hit Soundcheck and those files on disk are patched back to channels 1-5 (and your live inputs are not) so you can play them back and adjust levels how you like them while the band does something else.
When you’re ready to play live again, turn Soundcheck off and all of the inputs are patched back how you had them but now you have a great mix ready for the show.