What makes one element more reactive than another?

It's not a simple question!

You should have a complete knowledge of atom's quantum mechanics. 

For the moment, I can only say this: 

Imagine to add one proton and two neutrons to hydrogen nucleus and an electron around: you have helium atom. Why is it so different, chemically, from hydrogen? Electrons, at least inside an atom, are not little balls, instead they are sort of "waving clouds". These "clouds", among other things, shield the positive charge of the nucleus. With two electrons, the electronic clouds of helium are localized in such a way to shield very well the electric charge of the nucleus, so the electrons of another atom are not attracted from this positive charge. 
For this reason helium atoms are almost non-reactive chemically.

The opposite between two hydrogen atoms: the charges of the nucleus are badly shielded and when two hydrogen atoms, for example (or an hydrogen atom with a chlorine atom or many other kinds of atoms) approach each-other, the electron of one atom is attracted from the nucleus of the other, generating a Very strong (covalent, in this case) bond between the atoms.

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