Question

Why boiling point of a liquid remain constant although heat is continuously supplied to the liquid?

Answer 1

Mind you...this is a bit simplicistic:

Explanation:

The energy you supply at boiling point through heat is used to basically "free" the molecules from their intermolecular connections (and become vapour) and it is used to increase the vibrations of the molecules until such vibrational average kinetic energy exceeds the intermolecular force strength, and it all becomes translational average kinetic energy (and the phase change is finished).

(That would allow for an increase the temperature of the entire system, but only after the phase change finished.)

Consider the molecules of your liquid like persons holding hands; the persons receive energy and vibrate (increasing the temperature) but at a certain point they use the energy to release the hands that connect each other becoming free (as a gas).

Considering a "sad" analogy: imagine you receive your salary (heat) directly into your bank account BUT you the bank also pays your bills directly...