A pin matrix replaces patch points with a neat grid, and replaces patch cables with pins.
With a modular synthesiser, there's no way to predict which combination of modules a user will put in their system, so they can only connect to each other using patch points accessed on each module itself, and busses that pass along to any module that will listen some generally useful signals (usually a CV/gate pair for the note's pitch and length).
In contrast, as a semi-modular synthesiser has a set configuration, its designers know exactly which patch points it's going to have. This lets them group all the patch points together into a handy patchbay, as with the MS-20.
Taking this a step further, a pin matrix turns this into a simple two dimensional grid: one axis represents outputs, the other inputs. By placing a metal pin where an output intersects with an input, it connects the two together.
Each output can connect to many inputs, and (if the system has appropriate protection) each input can connect to many outputs, simply by adding more pins along the same row or column. This is a much tidier solution than Moog's multiples and attenuator modules, and even Buchla's stackable banana jacks.
There are a few drawbacks. Most notably, unless some of the rows and columns are connected to regular jacks round the back, this is a closed system, whereas patch points let you connect multiple modular and semi-modular synthesisers to each other (even if they were never designed to let you do that). Also, there's no normalling to set a sensible default route, as everything has to default to being disconnected.
Personally, I also find it easier to see what's connected to what by following patch cables, as they're less abstracted... but a pin matrix is certainly tidier.
Signal routing: Phone jack | Pin matrix