When a liquid is heated in an open vessel, its temperature and vapour pressure will both increase. At the temperature at which the liquid's vapour pressure (the pressure at any given temperature at which both liquid and vapour are in equilibrium) would be equal to the external pressure, vaporisation can occur throughout the bulk of the liquid, and free expansion of the gas into its surroundings may take place. This free vaporisation of the liquid throughout its bulk is what we call boiling, and the temperature at which it occurs is called the boiling temperature or boiling point.

Note the requirement for the external and vapour pressures to be equal for boiling to occur explains the well-known phenomenon of liquids boiling at lower temperatures at higher altitudes (where the atmospheric pressure is less than at sea level). With a lower external pressure, the vapour pressure of the liquid does not need to be raised by as much to equal it, and consequently less heat needs to be supplied to bring about boiling.
It is worth introducing some definitions here:

The normal boiling point, T_b, is the boiling temperature when the external pressure is one atmosphere.

The standard boiling point is the boiling temperature when the external pressure is is one bar

Since one bar is slightly less than one atmosphere, the standard boiling point of a liquid is slightly less than its normal boiling point. (Note that the difference in pressure between 1 bar and 1 atm has been exaggerated in the diagram for clarity.)

Boiling does not occur when a liquid is heated in a closed vessel. The vapour pressure of the liquid rises, but as a consequence of the vaporisation that occurs from the surface of any liquid while it is being heated, the density of the vapour in the vessel also increases.  (In effect, we may consider that while the vapour pressure of the liquid is rising, the extra vapour that evaporates increases the  pressure upon the liquid. The vapour pressure thus never reaches the same value as the external pressure, because both values are increasing as a result of the heating. This problem does not arise in the open vessel because the vapour that evaporates is free to disperse, and the external pressure upon the liquid thus remains constant throughout.)

Heating also causes expansion of the liquid, and thus a reduction in its density, and eventually a point comes where the densities of the liquid and vapour are equal. At this point, the surface between the two phases vanishes, and the container is filled with a single uniform phase called a supercritical fluid.

The temperature at which the surface between the two phases disappears is called the critical temperature, T_c, and the vapour pressure at the critical temperature is called the critical pressure. The point on a phase diagram corresponding to the critical temperature and pressure is called the critical point. Note that at and above the critical temperature, the liquid phase does not exist - it is replaced by the supercritical fluid.

The triple point of a substance marks the set of conditions under which three different phases of the substance (typically solid, liquid and gas) all exist in equilibrium with each other. It is the point on a phase diagram where three phase boundaries meet. The temperature at the triple point is denoted T₃ .

The triple point of a pure substance occurs at a single fixed pressure and temperature, characteristic of the substance. For example, the triple point of water occurs at 273.16 K and 611Pa.

Note that the triple point marks the lowest pressure at which the liquid phase of a substance can exist. If the solid-liquid phase boundary has a positive gradient, as is almost always the case, then it also marks the lowest temperature at which the liquid phase can exist.