Interlinking
Interlinking is where systems connect to each other in a big web. These are the key to interesting strategy in games. Let me explain.
An example
My orc attacks your orc. I roll a die, and if it's higher than your defence, your orc dies.
This system is self-contained, and boring. There's no strategy here.
If you link an action to something in another part of the game, it becomes too difficult to solve, and the player must use their judgement. This is interesting for the player.
Let's try an interlink.
My orc attacks your orc, and kills it. To do this, I must also discard two cards from my hand.
This interlinks combat into the game's card system. It's an interesting trade-off, without an obvious answer. I'd need to know the exact value of the cards, which is probably too complicated to work out. And, they probably interlink to other things too.
Another example:
My two orcs attack your orc, and kill it. My attacking orcs return back to their home village, in a different part of the board.
This one interlinks combat into the game's spatial system. Maybe you need the orcs in this part of the board, and there are other things for them to do. Again, this creates an interesting choice.
You do need to interlink out to something complex, or your puzzle will still be solvable.
If you can't interlink, then your game probably doesn't have enough systems, or a system deep enough. Add one.
Two systems
Many games revolve around a giant interlink between two systems, and it works. A common combination is to have one part of the game be spatial, while the other is a competitive resource-gathering area that isn't spatial. Those are so different that it creates a problem that's impossible to completely solve.
In Agricola, the systems are the competitive central task board, and each player's own farm, which is spatial.
Eight-Minute Empire is a stark example of two interlinking systems. Players simply take a card from the card row on their turn, and follow its instructions. These cards move their armies around a board, or create new armies. Gaining control of the board gets the player points. However, these cards also have a colour, and picking many cards of the same colour awards lots of points at the end of the game. This simple interlink creates an unsolvable problem, and therefore an interesting game. Do I take a card, to help me take over the map, or to try to collect a certain colour?
Biblios is a good game, but it lacks proper interlinking at the start of the game. On your turn, you draw five cards, but one at a time. You choose one to keep, three to give the other players, and one to put into a future auction. The problem here is that the strategy is too simple, and solvable — as you go through the five cards, you just take a good one (or an average one if you're near the end of the five cards). There's an interlink out to the game's coloured-card collecting system, but you don't have any other cards yet, so that interlink doesn't do anything.
Core systems
A properly-functioning core is essentially a group of interlinked mechanics that are too complex for the players to completely figure out.
The more complex the system, the more interlinking works.
Some games hide information (such as an unknown hand of cards), creating a statistical calculation that's too complex to solve. Others use randomness, which barely works, as it's usually too simple. (It also has unrelated downsides.)
One of the systems can be a complex human system, such as psychology, negotiation, or physical dexterity. Interlinking to these will create huge depth.
Scrabble interlinks a spatial system (a grid) and the dictionary, both of which are highly complex. The result is a game I've been playing for decades.