A liquid remains in its phase because the intermolecular forces between adjacent particles are strong enough to hold them together. Within the liquid, each molecule is attracted to other particles surrounding it in all directions. At the surface, molecules of the liquid aren't completely surrounded by other liquid particles. Factors influencing the behavior of the liquid particles at the surface are their kinetic energy, intermolecular attractions to other liquid molecules, and atmospheric molecules above them exerting pressure. If the intermolecular attractions are very strong, as in hydrogen bonding, then the liquid will have high surface tension. If the intermolecular attractions are weaker then it will have a higher tendency to evaporate at the surface. As the temperature increases so does the average kinetic energy of the particles so at higher temperatures intermolecular attraction will be less of a factor and there will be more evaporation.
The pressure that vapor molecules from the liquid exert at the surface is called vapor pressure. It increases with temperature. Boiling occurs when the vapor pressure reaches atmospheric pressure.