Surely a wave needed something to wave in
Water waves need water and sound needs air. Nineteenth-century physicists therefore imagined a luminiferous ether carrying light. As Earth moved through it, light sent along and across the supposed ether wind should take slightly different times.
Albert Michelson split a beam into perpendicular paths and recombined them. A difference in travel time would move the interference fringes.
Diagram description
Animated physics diagram: michelson_morley_interferometer; showing time.
The stubborn null result
In 1887 Michelson and Edward Morley floated the apparatus on mercury so it could rotate smoothly. The expected fringe shift did not appear strongly enough to support the simple stationary-ether model.
The experiment did not instantly prove relativity, and Michelson did not immediately abandon ether. Instead, a reliable null result steadily reduced the room available to older explanations. Sometimes the fact is not what an instrument sees, but what a sufficiently sensitive instrument repeatedly fails to see.