A crystallite is a domain of solid-state matter that has the same structure as a single crystal.
The crystallised matter is rarely found as single crystal, except for a few cases (gems, silicon single crystals for the electronic industry, single crystals of a nickel-based superalloy for the military aircraft engines). Most of time, it is polycrystalline, i.e. it is made of plenty of single crystals - the crystallites - that "stick" together. The crystallite size can vary from a few nanometers to several millimeters.
Metallurgists often refer to "grains"; thus, the boundary between two crystallites is the grain boundary, the fracture can be an intergranular fracture or a transgranular fracture. But there is an ambiguity with powder grains: a powder grain can be made of several crystallites. Thus, the (powder) "grain size" found by laser granulometry can be different from the "grain size" (in fact: crystallite size) found by X-ray diffraction (e.g. Scherrer method), by optical microscopy under polarised light or by scanning electron microscopy (backscattered electrons).
Therefore the term "crystallite".
But the term "crystallite boundary" does not exist, it is "grain boundary".