Homogeneity in physics means that something is the same throughout. Let's say you have a cake that you cut into two pieces, but both pieces are exactly the same. That means the cake is homogeneous.
In physics, things can be homogeneous in many different ways, like how the temperature is the same throughout a room, or how the density of a material is the same throughout.
Think of a bowl of jellybeans. If you mix them all up really well, and then you take a handful of jellybeans, the chance of each individual jellybean being a certain color is the same as any other color. This means that the jellybeans are homogeneously mixed.
When something is homogeneous, it allows physicists to make easier predictions about how that thing will behave or change over time.