Step 1: Intermolecular forces govern boiling point.
The boiling point of a liquid depends on the strength of intermolecular attractive forces. For non-polar or weakly polar compounds, London dispersion (van der Waals) forces are dominant.
Step 2: Factors affecting London dispersion forces.
London dispersion forces increase with (a) increasing molecular size and surface area and (b) increasing polarisability of the electron cloud. Larger, more polarisable electron clouds create stronger instantaneous dipoles.
Step 3: Variation across halogens F to I.
Atomic radius and polarisability both increase from F to I. Iodine has the largest, most polarisable electron cloud; fluorine has the smallest and least polarisable. Therefore $RI$ molecules attract each other more strongly than $RF$ molecules.
Step 4: Conclusion on boiling point order.
Stronger intermolecular forces require more energy to overcome during boiling. Hence the boiling point increases in the order $RF < RCl < RBr < RI$, which explains why $RI > RBr > RCl > RF$.