First, I have a few answers that discuss this in gory detail (i.e., why area affects flow speed for sub- and supersonic flow) at: https://physics.stackexchange.com/a/612590/59023 and https://physics.stackexchange.com/a/524215/59023.
A nozzle is a device that increases the velocity of a fluid in the expanse of pressure energy drop of the fluid (The Bernoulli principle).
I would not think of this in terms of Bernoulli's principle, per se. Perhaps try the following line of reasoning. The thermal speed of the particles in a collisional medium like Earth's atmosphere is roughly the speed of sound. If you "bunch up" those particles, you just force them to collide more often.
Suppose you start with a bulk flow through a pipe and ignore friction with the walls of the pipe for now. Note that the bulk flow is the different from the random kinetic energy associated with pressure (e.g., see https://physics.stackexchange.com/a/218643/59023). That is, the bulk flow of any fluid is independent of the thermal speed of the fluid for most situations. In the case at hand, the bulk flow is subsonic. Under these conditions, the flow of the fluid can be approximated as incompressible. That is, we can assume the continuity equation (i.e., mass flux conservation) holds so that an increasing area results in a decreasing bulk flow speed.
So the physical reasoning behind this is that the same amount of fluid must flow past a given length of pipe in the same unit time. That means that the area times the speed of the flow is a constant, so if the area increases, the flow speed must decrease accordingly. If this were not the case, little vacuums would develop in the flow. It's like having a constant volume filling rate in order to avoid developing little vacuums in the pipe.
Now how can we explain (conceptually, no math) why a subsonic nozzle shape (a convergent channel) is different from a supersonic nozzle shape (a divergent channel)?
If the flow starts out supersonic, the flow is now compressible because the bulk speed is comparable to or larger than the average random speed of the particles in the fluid rest frame. That is, if the flow runs into any normally incident obstacle, the particles will not be able to "get out of the way" before being hit by a trailing particle. This will cause a "pile up" of particles that could eventually lead to a shock wave.
So when supersonic flow enters a divergent region (i.e., increasing cross-sectional area), the faster particles, which were previously running into the slower particles in the group, can now "escape" more easily. This will cause the bulk flow to accelerate as the faster particles in the trailing parcel of fluid will "push on" the slower particles in that parcel. Since the leading parcel is already supersonic, this "pushing" can actually move the slower particles in the trailing parcel ahead without worry of ramming into the leading parcel.
Similarly, if a supersonic flow runs into a constriction (i.e., decreasing cross-sectional area), the trailing particles will ram into the leading particles because the leading particles are reflecting off of the pipe walls back into the incident particles. The result will be a compression and deceleration of the flow.