There are so many things that rely on solids having a definite shape and volume, it is impossible to cover them all.
To start with, if our bones (a solid) did not have definite shape, we would be unable to move with the speed and agility we have. We would have to creep along the ground like a slime mold, as our bodies would take the shape that gravity dictated. But even that relies on earth being solid, otherwise the earth would cease to be a sphere and become a weird shape with the heaviest areas sinking in, and the lightest distending to compensate. And that's only if the earth had a definite volume. If the Earth had no definite volume, then it would become a nebula held together only by the weak gravitational attraction between individual molecules.
Structures are made primarily with solids. If building materials didn't have definite shape, winds would flatten structures in an instant, and thus provide no shelter from certain weather conditions.
Life without solids would be so different. Eating would be impossible as there would be no solid food, and our stomach would be an indefinte mass of digestive juices. Plant life would be nonexistent. The universe itself would go back to it's beginings as a mass of mixing gasses.
It would be really inconvenient for solids to easily change state. I don't even think people would be able to survive or even exists because our body and organs would just turn into liquid or gas, which would be difficult to control. We wouldn't have solid objects like phones or TVs or cars, and all food would be liquid in our stomachs. Really, I don't think it'd be possible to survive.