Water is polar, meaning one part of the molecule is more positively charged and the other is more negatively charged. This makes it interact very well with charged (or other polar) things, making it good at dissolving them.
There are other polar solvents, like ethanol, that can, to an extent, dissolve many of the same things water can.
The reason we think of water as a near universal solvent is because it is both very polar and very common.
That said, water is pretty useless at dissolving non-polar things like grease. This is why we have non-polar solvents as well as surfactants (i.e., soap). Surfactants are molecules that have a polar and non-polar end which helps water dissolve non-polar molecules.
We are made from water, so we and stuff we usually interact with work pretty well with water. The stuff is also very common around the universe, so it is easy to come by.
The special properties that matter come mostly from being _polar_, it having some tiny-magnet-like* properties that makes it attract more of itself and other substances such as salts. As a consequence it dissolves things well, freezes relatively easily, and even expands when freezing. All those have benefits for life. Hence why nature ended up using water.
But there are potential alternatives, they are just less common in the universe and/or less optimal. There are also stronger solvents than water, but being too strong of a solvent also has disadvantages (imagine it dissolving your skin, for example!).
*: not actually magnets, but close enough for ELI5; it’s electric charges, though.
Water is made up of a single oxygen atom flanked by two hydrogen atoms. The hydrogen atoms each share their single electron with the oxygen. Due to the arrangement and configuration of electrons in the oxygen atom, the way in which it shares these electrons causes the molecule to be “bent.” So the oxygen atom sticks out a bit and the hydrogen atoms stick out a bit the other way.
The side with the oxygen atom is where most of the electrons congregate, and therefore has a negative charge. The side with the hydrogen atoms then has a positive charge. This basically means that water molecules are like tiny magnets. This rather simple fact is what gives water a lot of its amazing properties (such as the fact that its solid form, ice, is less dense than its liquid form).
Because of this arrangement, we call water molecules “polar” and it allows it to attract and stick to a wide variety of other kinds of molecules. If the other molecule is negatively charged? The hydrogens grab it. If it’s positively charged? The oxygen grabs it. Basically anything else that is also polar (which is a great many things) can be dissolved by water.
This means that things that are non-polar do not dissolve well (if at all) in water for example, oil. This is why we can add things to water, like soap, to help with this. Soap is a very complex molecule that has one end that is good at sticking to water and another end that is good at sticking to fatty things like oils. So the water grabs the soap and the soap grabs the oil and allows you to wash it away.
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