That's tough to answer without just saying, "That's just the way it is." But I'll do my best.
At a basic level, all of waters properties comes from the combinations of the properties of its constituent particles and the way they interact with each other and other atoms/molecules. The main reason water is less dense as a solid than as a liquid is because of the way its electrons are configured and shared. It has two lone pairs that repulse both each other and the electrons shared in the bond between the oxygen and hydrogen atoms, giving rise to the 'bent' shape of the molecule. The high electronegativity of oxygen causes the hydrogen atoms to be positively charged, as oxygen attracts the bonded electrons more strongly than the hydrogens do. This gives rise to a fairly strongly polarized molecule, with the oxygen atom having a relatively high negative charge and the hydrogen atoms having a relatively high positive charge. This, in turn, leads to the strong attraction of the hydrogen atoms to the oxygen atoms (and a repulsion of oxygen-oxygen or hydrogen-hydrogen), which, when combined with their bent shape, causes ice to have large open spaces between groups of water molecules, making it less dense than liquid water.
I also think a great deal of it has to do with water's simplicity. Water is only composed of three atoms, and isn't complex enough for a lot of other effects to occur that might be detrimental to us. Water cannot be bent into different shapes like larger, more complex molecules can. Its atoms all have relatively few electrons and a small size, making it easy to polarize the molecule, which has the effects I mentioned above. It can also easily be used as the basis for larger compounds by means of forming a hydroxyl group (-OH) that gets attached to a substantial number of other molecules in living organisms.
The bonding of hydrogen and oxygen is itself a combustion process, meaning that water has, in a sense, 'already been burned', so it's in a low-energy state that is difficult to transform into something else. Ripping an atom off of this simple molecule usually makes it want to quickly re-bond to form water again and not another, different molecule.
Compare this to something like a complex molecule of the alkanes, which are a group of molecules that are composed of carbon bonded to both hydrogen and itself, specifically in that each carbon shares a single bond to another carbon. They can form a long string or a complex shape that allows larger molecules to be broken apart into many different forms, each with different properties.
Hydrogen and carbon are also both able to bond with oxygen, a common atom in our environment, to form lower energy states in the form of things like water and carbon dioxide. But there isn't another atom that hydrogen or oxygen can bond with to make a lower energy state that's common in our environment. Fluorine is perhaps the only other atom that hydrogen can bond to that would put it in a lower energy state, but fluorine is nowhere near as abundant as oxygen.
Water's polarized nature also lets it dissolve many other substances, a crucial feature for biology. Yet, because of its already low-energy state and the high bond strength between oxygen and hydrogen, it isn't particularly corrosive, so even though it can dissolve a large number of substances it won't break most of them down by itself at any appreciable rate. That is, molecules might disperse into a solution of water, but the water won't break the molecules down very rapidly, if at all, another key feature for biology. It wouldn't do any good to build a bunch of proteins and other molecules if the very solvent they were in simply ripped them apart again.
The specific difference to other hydrogen-bonding molecules is that in water the hydrogen bonds with a lone oxygen atom. The combination of oxygen's small size, low number of electrons, particular electronic configuration, and number of protons gives it the properties that make water unique versus other molecules with hydrogen in them.
