An aperiodic monotile (sometimes called an "einstein") is a shape that can tile the plane, but every such tiling is necessarily non-periodic. In layman's terms, it is a tile that can be used to cover a flat surface without any overlapping or gaps, but does not show any periodic repetition.
A famous example is the "hat" aperiodic monotile, discovered in 2023 by David Smith, Joseph Samuel Myers, Craig S. Kaplan, and Chaim Goodman-Strauss. The "hat" tile forces aperiodicity in the plane; however, all tilings by the hat require both mirror images of the tile to appear. Later in 2023, the same authors published a paper presenting the discovery of a "spectre" aperiodic monotile, which tiles aperiodically using only translations and rotations, even when reflections are permitted.