What is Spontaneous Symmetry Breaking?
At every point in space, the Higgs field has a certain strength, a number that tells you how active the field is. This is quite similar to temperature: You can assign a temperature to every point in a room, and the temperatures might be different for different points in the room and even change with time.
The Higgs-Englert field is the most special fundamental field that we know of: It interacts with nearly all of the other fields (like the electron field or the quark fields). This means that the Higgs field can greatly influence the other fields: If it is active somewhere, then electrons, quarks and other particles in that region will be slowed down by it. This is equivalent to them gaining mass!
But if the Higgs field would have an average strength of zero (as is usual for a field), then we would not be able to observe this slowdown (meaning no mass for other particles).
So how come this is not the case? It turns out that the Higgs field's potential, which governs how much energy is needed to increase its strength, has a very special form (see below). If the energy density in the universe is low enough, the field will drop down into the valley in the potential. This means it will be locked to a non-zero strength, and other particles gain mass everywhere in the universe!
Source: Flip Tanedo