In thermal power generation, not all of the primary energy of the fuel is converted into electricity (the conversion efficiency being a measure of how much). The rest stays as heat which, in most cases, is wasted (e.g. it’s removed in cooling towers).
In a CHP process both power (i.e. electricity) and heat provide useful outputs: electricity into the grid and heat into a district heating system, for example. Hence more of the primary energy content of the fuel is being used (which you can regard as a higher efficiency) and the process has an additional economic output (which is helpful, given that the fuel presumably cost money to buy).
CHP is also described using the term cogeneration.
As an extension of CHP, there is also Combined Cooling Heat and Power (CCHP, or trigeneration). In trigeneration, heat can be converted using a technology known as absorption chilling in order to provide cooling. This cooling could make use of a fixed portion of the available heat, or could be adjusted to use varying proportions according to the season – for example focusing on heat production in winter and cooling in summer.