A flowing liquid speeds up at a pipe contraction because of mass conservation:
$$\dot m_1=\dot m_2\qquad\Leftrightarrow\\
\dot V_1\rho=\dot V_2\rho\qquad\Leftrightarrow\\
\dot A_1v_1\rho=\dot A_2v_2\rho\qquad\Leftrightarrow$$
$\rho$ is constant if the liquid is incompressible. So speed increases for decreasing $A$.
When something speeds up, that means a gain in kinetic energy. Energy conservation states that such energy must come from somewhere:
If there is no pump along the way, there is no external work done, $W=0$. Then the fain in the liquid kinetic energy must be taken from some other kind of energy, most likely a potential energy in some other form.
Pressure as energy
Pressure can be described as an energy form - we could call it mechanical potential energy - because:
$x$ is how far the liquid particles move while they accelerate to speed up. Such acceleration must mean that a force pushes them forward, and this force $F$ (which is essentially the push from the liquid particles behind) is doing the work $W$.
This "pressure energy", the mechanical potential energy due to pressure, is basically the combination of all the molecular kinetic energy of the liquid particles.
(We can call this mechanical potential energy because it is a driving factor for the motion, where particles always move towards lower potential (just like things fall towards lower gravitational potential energy and charges move towards lower electrical potential energy etc.)
Pressure as molecular collisions
All in all the gain in kinetic energy is thus taken from this "pressure energy". To increase the net flow speed, the individual random motion of the liquid particles decreases.
Less random motion means smaller pressure, because pressure - as you said - comes from the particles colliding with the pipe walls.