What does β stand for in β-potassium zirconate?
They signifies one polymorph (the beta polymorph) of barium zirconate.

Allotropy is the property of some chemical elements or compounds to exist in two or more different forms, in the same physical state at different temperature. Now, technically they are the same element or compounds but have different crystal structure at changing temperature. So, in order to name them, alpha, beta, gamma etc. are used in the prefixes to depict them as they are the allotropes formed at different temperature phases.. That helps in their differentiation.

For e.g. iron has 5 allotrope namely:


ferrite (α-iron): the ferromagnetic form at T &lt; 770 °C (the Curie point, TC); BCC crystal structure
β-iron: T = 770 – 912 °C; the paramagnetic form of α-iron; same structure as α
austenite (γ-iron): 912 – 1,394 °C; FCC crystal structure
δ-iron: 1,394 – 1,538 °C; forms from cooling down molten iron; same structure as α
ε-iron (also called hexaferrum): forms at high pressures; HCP crystal structure


There are several more examples of such type of nomenclature of elements. You can find them in the wikipedia article of allotrope(see table).

Also, not only elements form allotropes. Compounds also form allotropes but have a different name i.e polymorphs. Generally, binary metal oxides are polymorphs. Polymorphs have different temperature phases in which one form of crystal structure exist. These phases are depicted by giving greek alphabet at the prefixes like α-phase, β-phase etc. Polymorphs or allotropes of compounds are given that greek alphabet prefixes according to that phase in which one form of that compound exist.

For e.g. iron oxide $\ce{Fe2O3}$ has 4 phases.


α-phase: at ambient conditions: has Corundum-type Rhombohedral (R3c) like structure
β-phase: below 773 K: has Body centered cubic (Ia3) like structure
γ-phase: up to 933 K: has Cubic, spinel structure (Fd3m) like structure
ε-phase: has Rhombic (Pna21) like structure


So, iron oxide $\ce{Fe2O3}$ has 4 polymorphs : $\ce{\alpha-Fe2O3, \beta-Fe2O3, \gamma-Fe2O3, \epsilon-Fe2O3}$.

For more information you can check this question(asked by myself) or this question that describes how polymorphs is formed.