This is a more QM answer, there is a main difference between solids and liquids:
solids do have a lattice structure, where the relative position of atoms/molecules is mostly fixed. This is caused by covalent bonds, meaning that the valence electrons around each separate molecule start existing around multiple molecules/atoms, thus creating a EM bond between the neighboring molecules and thus fixing their relative position
liquids do not have such a lattice structure, the liquid molecules have something called the van der waals force, that bonds them into droplets, and all molecules have the ability to roll over each other thus creating the liquid effect. Now in liquids, there is no covalent bond between molecules, the valence electrons do not exist around both molecules, thus the neighboring molecules do not have a fixed relative position.
Now Feynman is connecting this to temperature. The reasoning is, that the vibrational energies of the molecules (that we can interpret as temperature), decreases as we decrease the temperature of water.
As you keep decreasing the temperature, you reach a point where the lattice structure starts being created, that is, the valence electrons around the molecules start existing around both neighboring molecules, thus creating a covalent bond between the molecules. Thus, the molecules relative position is fixed, and this has to do with the decrease in vibrational energies of the molecules (jiggling around).
As the molecules spend less and less time jiggling around, they allow for the valence electrons to spend more and more time around both molecules. It is QM, and all about probabilities, where the valence electrons do have some probability of existing around both molecules always.
This probability is what is increasing as the molecules position becomes more and more relatively fixed, as the jiggling around decreases. At a certain point, the molecules spend more and more time at a relatively fixed position, and this will allow for the valence electron to exist around both molecules at higher probabilities, thus creating a covalent bond.