Generally, homogeneity means being the same throughout. For various specialized meanings, see:
Homogeneous (mathematics), a variety of meanings
In statistics homogeneity can refer to

• Homogeneity of variance: Homoscedasticity
  Logically consistent data matrices: homogeneity (statistics)
  homogeneity (physics), in physics, two particular meanings: On one hand, translational invariance. On the other, homogeneity of units in equations, related to dimensional analysis
  Homogenetic or homoplastic, in biology, applied both to animals and plants, of having a resemblance in structure, due to descent from a common progenitor with subsequent modification [1]
  Homogenization is intensive mixing of mutually insoluble phases (sometimes with addition of surfactants) to obtain a soluble suspension or emulsion, for example homogenizing milk so that the cream doesn't separate out
  In physical chemistry, homogeneous describes a single-phase system as opposed to a heterogeneous system. See also phase diagrams and the classification of catalysts
  In the context of procurement/purchasing, homogeneous is used to describe goods that do not vary in their essential characteristic irrespective of the source of supply