How do water's relative densities as a solid and a liquid differ from that of most other substances?
Under normal ambient conditions water is less dense as a solid than as a liquid, so ice floats on water. Most materials are more dense as solids.
When water freezes, the molecules do not stack into a close-packed structure. They form a relatively open, honeycomb-like arrangement (image source: https://www.nyu.edu/pages/mathmol/textbook/info_water.html).
The extra volume in this honeycomb structure, which the liquid does not retain with its mobile molecules, is responsible for water ice being less dense than liquid water.
We can force the ice into a denser, more close-packed structure by applying high pressure, hundreds of atmospheres or more. These structures are more dense than the liquid at the same pressure. Scientists have identified more than a dozen of these high-density ice phases (https://en.wikipedia.org/wiki/Ice).
While water is unusual, it is not unique. Elemental silicon forms a relatively open, tetrahedral structure when solid, and as with water the extra volume in this structure makes solid silicon less dense than the liquid.