a single crystal
A single crystal is one unbroken crystal, a piece of material in which the same repeating atomic pattern runs, in the same orientation, from one side clean through to the other, with no interruptions. Gemstones are the familiar picture: a well-formed quartz or diamond is (ideally) one crystal throughout, which is why it can have flat, mirror-smooth natural faces meeting at fixed angles.
In a single crystal there is a single, continuous lattice orientation everywhere, no grain boundaries dividing it into misaligned patches. Contrast this with a polycrystal (like ordinary metal), which is a mosaic of millions of tiny crystals stuck together at random angles. Because a single crystal has one orientation, its direction-dependent (anisotropic) properties show up plainly: it may be stiffer, or conduct better, along one crystal direction than another.
Single crystals are grown deliberately when directionality or perfection is essential. Silicon chips are cut from single-crystal wafers because grain boundaries would scatter electrons and ruin the devices. Jet-engine turbine blades are cast as single crystals so there are no grain boundaries to creep or crack at high temperature. Single crystals are also what crystallographers most want for structure solving, since one clean lattice gives the cleanest diffraction. Caveat: even a single crystal contains point defects and dislocations, single means one grain orientation, not literally flawless.
A silicon wafer is cut from one single crystal so electrons travel unimpeded; a turbine blade is cast as a single crystal so that at high temperature there are no grain boundaries to creep or crack. One orientation is exactly why they are grown this way.
A single crystal: one lattice orientation throughout, so anisotropy shows fully.
Single crystal means one grain, not zero defects. A single crystal can still hold vacancies, dislocations, and impurities; what it lacks is internal grain boundaries.