The definition of boiling point is given on p. 694. The boiling point is the temperature at which the vapor pressure of the liquid equals the external pressure. In an open system, like in most laboratory setups, the external temperature is the atmospheric pressure. The normal boiling point is defined for an external pressure of 1 atm, or 760 mm Hg.
The above also means that the boiling point of a substance under vacuum is lower than the boiling point of the same substance in an open system. For example if diethyl ether, which has a normal boiling point of 35-36o C, is exposed to vacuum, it can boil at room temperature. A system under vacuum is sometimes said to be under reduced pressure.
Fig. 13.3 on p. 696 shows the method that will be used in the lab for determining boiling point. The student takes a small test tube, about the size of an average little (or “pinky”) finger. Place about 1 mL of liquid in the test tube and start heating. When the liquid boils and a reflux ring forms above it, insert the thermometer deep enough for the tip to be inside the refluxing vapor, but without touching the boiling liquid. Allow for temperature stabilization. When the temperature reading becomes constant, record the boiling point.