(1) Of the same or a similar kind. (2) Of uniform structure or composition throughout.
Example:
Though she was raised in a small town, she liked living in the city because the population there wasn't so homogeneous.
A slab of rock is homogeneous if it consists of the same material throughout, like granite or marble. A neighborhood might be called homogeneous if all the people in it are similar, having pretty much the same background, education, and outlook. Homogeneity is fine in a rock, but some people find it a little boring in a neighborhood. Foods can be homogeneous too. Milk, for example, is homogenized so that its fatty part, the cream, is spread evenly throughout, giving the milk a consistent, homogeneous texture.