In one "word", the strength of the intermolecular forces of attraction.
Sulfur, phosphorus, and chlorine vary in the size of their respective molecules; out of these three, phosphorus has the largest molecule, followed by sulfur and chlorine.
These molecules only exhibit weak van der Waals interactions, or London dispersion forces (LDF), the strength of which depending on the size and shape of the molecules.
LDFs are very weak because they depend on the random distribution of electrons around a molecule at a given moment. When electron clouds get distorded by this random variation in the distribution of electrons, temporary dipoles appear.
When one such dipole appears in a molecule, that molecule is able to polarize the electron cloud of a neighbouring molecule
So, the bigger the molecule, the bigger and denser its electron cloud will be, which means that the temporary dipoles that appear will be a little stronger.
So, in order to melt phosphorus, sulfur, and chlorine all you have to do is break these very weak van der Waals interactions, which explains why sulfur, the bigger molecule of the three, will have the highest melting point, and chlorine, the smallest of the bunch, will have the lowest.
Read more on LDFs here: