Short answers, pulled from the story.
Length contraction is the phenomenon by which a moving object's length, measured along its direction of travel, is shorter than its proper length, which is the length measured in the object's own rest frame. The effect is described by the Lorentz factor and only becomes significant at speeds that are a substantial fraction of the speed of light.
George FitzGerald proposed the contraction hypothesis in 1889, and Hendrik Antoon Lorentz independently proposed it in 1892. Both were attempting to explain the negative result of the Michelson-Morley experiment and preserve the hypothesis of a stationary aether, which is why the effect is also called the Lorentz-FitzGerald contraction.
Lorentz believed length contraction was caused by the physical compression of atoms in a moving object and required no change to the fundamental nature of space and time. In his 1905 paper on special relativity, Einstein declared the aether superfluous, removed the concept of absolutely stationary space, and showed that contraction is a geometric consequence of the structure of spacetime itself, not a physical squeezing of matter.
Length contraction is a measurement of an object's endpoints taken simultaneously in a given frame. A photograph, by contrast, captures light that left different parts of the object at different times. As James Terrell and Roger Penrose showed independently in 1959, this light-travel-time effect means a moving object does not appear contracted in an image but instead appears rotated, a result now called Penrose-Terrell rotation.
Magnetic attraction between parallel wires is a result of relativistic length contraction. In the reference frame of the drifting electrons, the protons in the opposite wire are in motion and appear contracted, making them locally denser. This creates an apparent charge imbalance that produces an attractive force, even though electron drift velocities are only on the order of a meter per hour.
Indirect evidence includes the negative result of the Michelson-Morley experiment, the survival of muons from the upper atmosphere to Earth's surface (explained by atmospheric length contraction in the muon's frame), the flattened shape of heavy ions in particle colliders, and the short wavelengths of synchrotron radiation in free-electron lasers, which can only be accounted for using length contraction in the electrons' rest frame.