At the boiling point, the liquid and gas phases are in equilibrium. What does that mean? Let's take a moment to go into a bit of depth.
The equilibrium balance of liquid and gas occurs when there is an equal probability for the distribution of matter and energy for the system and surroundings, an equal probability for heat to flow in to form the vapor or heat to flow out and result in condensation. This is another way of saying that the free energy of the liquid and gaseous phasese are equal. Under the precise thermodynamic conditions of pressure and temperature at the boiling point neither state is favored. At the equilibrium point, there is an even chance that what occurs here is being undone over there. If energy flows this way, it is just as likely to flow the other way. For the boiling liquid, the randomness of gas molecules makes the formation of gas likely to happen, but there is also likelihood in heat dissipating out into the surroundings when gas condenses to form liquid. At the boiling point, the conditions of temperature and pressure make each direction equally probable.
But if you increase the pressure, you increase the free energy of the gas relative to the liquid, and so condensation occurs. The change occurs in the direction that leads to a free energy decrease. What happened when you increased the pressure, actually, is that you increased the stakes of the pressure-volume work in condensation. This means that the compression will correspond to a larger negative enthalpy change.
Similarly, increase the temperature and you will increase the free energy of the liquid relative to the gas, and so the vapor is favored at the higher temperature. At the higher temperature, you decresed the the entropy stakes of heat flow (remember, the entropy change due to heat flow, ΔS = ΔH/T). At higher temperature, equilibrium shifts more toward the endothermic direction.