Key to understanding the ability of freezing of water to break a pipe is the phase transition from liquid water to ice. Let me first discuss water freezing generally, and then I will go to the specific case of water bursting a pipe.
In ice crystal the water molecules are in a stabilized position. The stabilization comes from the formation of a particular type of bond that is called 'hydrogen bridge'. A hydrogen bridge is a much weaker form of binding than a molecular bond, but as we know: in the case of water there is a siginificant effect.
As with any form of binding: when molecules fall into a bond there is some release of energy. Conversely, once a bond is formed input of energy is required to break that bond.
At room temperature only a small percentage of the water molecules has a hydrogen bridge going on. At room temperature the thermal motion of the water molecules is vigorous enough to break any hydrogen bridge that forms. Hydrogen bridges do form, but they don't last.
The freezing point of water is the critical point. Below the freezing point the rate of formation of hydrogen bridges exceeds the rate of dissolution of hydrogen bridges.
When you have an amount of water, and you continuously withdraw heat then at the freezing point the graph of temperature versus time will flatline for a while. It's only when all of the water is frozen solid that the temperature starts dropping again.
Imagine ice crystal, in contact with liquid water. The water molecules do not all move at the same speed. Given how they are bumping into each other all the time there is a statistical distribution of speeds. All the time it is the slowest water molecules that get "stuck" to the ice crystal, forming hydrogen bridges. That is, of the available water molecules the lowest energy ones transition to the ice form. So the remaining water molecules are slightly more energetic than the average. In effect the process of freezing replenishes heat that is being withdrawn.
Now to the case of water in a pipe.
When the temperature is several degrees below freezing then the pressure increases because it is energetically favorable to transition to the ice crystal form.
A sufficiently strong pipe would prevent the water inside from freezing completely. Since ice has a larger volume than water: the higher the pressure, the higher the energetic cost of going from the liquid form to the ice form.
However, in the case of the pipes we're talking about here the amount of pressure that the freezing water can exert is more than the pipe can withstand, and the pipe bursts.