There are a few different "access" issues that get thrown together. Sorry, I don't have NEC specific references here, but this is based on a lot of Q & A I've read over the past several years:
Main breaker panels, subpanels and similar types of equipment need a very large area in front to be accessible - 30" x 36". This allows working space in front of the equipment. Flipping a breaker requires no space at all. Replacing a breaker requires very little space. Properly installing a new circuit requires a lot of space. Older panels often did not have this working space - aside from some other practical reasons, my new breaker panel is to the left of where the old fuse & breaker panels were because there was a laundry sink blocking access, and even for removing circuits, that lack of space made the job harder for my electrician than it would have been if the current code requirement had been met.
As I understand it, this means a breaker panel can't generally be inside a cabinet. It also has to meet certain height requirements (can't be so high that you need a ladder to reach the breakers).
Disconnects (required for certain hardwired equipment if the breaker is not in line of sight and within specified distance, for feeds into separate buildings such as a shed, etc.), GFCI (which can be together with a receptacle, together with a breaker or standalone) and similar equipment needs to be accessible without any tools (because you need to get to it quickly and easily when you really need it) and below a certain height (no ladder required to reach it). Practically speaking, this means that a GFCI-protected ceiling (or very high on the wall) receptacle has to have the GFCI protection someplace else in the circuit. But these types of things can be inside a cabinet (e.g., GFCI below the sink connecting to disposal and/or dishwasher). Definitely no tools.
Junction Boxes, Conduit Pull Boxes, etc.
Almost any place where wires are joined together (junction boxes, switch boxes, receptacle boxes, etc.) needs to have access to the wires with no damage to the building. This also applies, as I understand it, to conduit pull boxes because access is needed if a wire needs to be replaced. This does not mean "no tools" - after all, normally the covers of these boxes are screwed shut for safety! Plus fixtures (e.g., lights, ceiling fans) often need to be removed to access ceiling junction boxes. But the key is that normal access - e.g., replace a receptacle or switch, patch in a new cable to a junction box to power something else, etc. - does not require any damage to the building.
Part of this is planning for future use and for future users. For example, if a piece of plywood is screwed in place then it will be quite obvious to the original owner. The next owner may paint the whole house and now the screws are no longer visible. Then when access is required, it could easily become "cut into the wood" and a major repair.
There is one exception: There are certain types of splices permitted inside walls without a junction box. That can save a lot of time & trouble for certain repairs, with the presumption that these splices are super-reliable and won't need future access. But that is an unusual situation.
A lot of rules in code have to do with avoiding damage to wires inside walls, both because the damage will be hidden and the repairs will be a lot of work. With the exception of significant wire damage (rodents chewing through wires, nails or screws going through wires, flood damage), almost all electrical problems and work are in a junction box of some sort - so those boxes must be accessible.