...is a demonic kingdom of holes, a minefield of crevasses and booby traps. Even in the best studios ever it will be mislabelled, dirty, f**ked up and be the source of most of your woes should everything in the world be routed through it. My advice: Bypass it whenever possible. Assistants will whine and cry, but consider getting a few of your own cables made up with every likely permutation of connector you may need for an average session, write your NAME on them, look after them religiously, use them. Oh, and remember to take them home with you.
In theory, the patchy, that snake nest of wires somewhere near the desk or on the wall is the hub of all studio connections, and I'll explain a few basic things. There are generally three kinds: GPO, 1/4", and Bantam, or TT. GPO is an old British telephone connector about the same size as a 1/4" plug with a weird shaped tip. These connectors are usually bulletproof as they were made when things were made properly. They are also made of a kind of brass which tarnishes and makes for intermittent connections. 1/4 is the semi-pro in the room, basically, a stereo jack and we all know how reliably people wire jack plugs. The disadvantage of these two is physical size. Bantam ( or TT - "tiny telephone" ) is smaller, essentially a mini GPO plug and allows you to cram a lot of holes into a 19" rack.
There are Three types of connection usually configurable depending on how things are wired, or sometimes adjusted with a switch if you're fancy.
The first is the Normalled or "break" connection as in the signal is connected by the bay until you insert a jack which "breaks" the circuit, at which point the signal stops and goes wherever the patch cable goes. Simples! You might have your preamp outs normalled to your interface inputs for example.
The second is Half Normalled, or a "sniff" connection which allows you to take a part of the signal and send it somewhere else as well Most desk insert configurations work like this; the send on the insert can be used as a split (for parallel compression for example) or a direct out and the signal will still pass through the rest of the channel until the bottom jack is inserted at which point the signal only goes wherever you are patched.
Lastly, we have "through" connections which do as they say- simple pass signals through to whatever they are connected to with no fancy trickery.
Let's get back to the practicalities of the patchbay. Yes, it is convenient, but I am here to teach you about the practicalities of studio life, not some idealised version. Thanks to the patchbay, famous producer guy will get pissed off with you as the left overhead dies mid drum take and he doesn’t notice and you are the idiot that does. Hopefully, the drummer will screw up, and that is the time to address the problem as if it was a happy accident. Don't wiggle the jack in the patch bay to try to fix it during the take. Do it between takes, and before you do - turn the monitor volume WAY down. What you could do is spray half a can of contact cleaner in the bay daily before people arrive, OR leave everything the hell alone if things are working. Your choice. It is always worse in smoking studios as electrical contacts hate a thin layer of nicotine and tar on them. Famous producer guy will be the guy smoking. Go figure.
One world famous studio in the UK has only female XLR to XLR cables originally to stop people from stealing them. One producer I know only uses yellow microphone cables because he says they sound better. Another is famous for grading the cables A, B, and C by listening to them on day one of a session. Yes, a whole day of just listening to microphone cables. Now I don’t know about any of that, but get a couple of your own that you KNOW work, trust me. When things don’t work, it’s usually a cable or connector. You could also do worse than buy a cheap phase tester, and check your cables, you’d be surprised how often things are wired wrong, and it could save you some hassle.