The term endothermic process describes a process or reaction in which the system absorbs energy from its surroundings; usually, but not always, in the form of heat. The term was coined by Marcellin Berthelot from the Greek roots endo-, derived from the word "endon" (ἔνδον) meaning "within" and the root "therm" (θερμ-) meaning "hot." The intended sense is that of a reaction that depends on absorbing heat if it is to proceed. The opposite of an endothermic process is an exothermic process, one that releases, "gives out" energy in the form of heat. Thus in each term (endothermic & exothermic) the prefix refers to where heat goes as the reaction occurs, though in reality it only refers to where the energy goes, without necessarily being in the form of heat.
Endothermic (and exothermic) analysis only accounts for the enthalpy change (∆H) of a reaction. The full energy analysis of a reaction is the Gibbs free energy (∆G), which includes an entropy (∆S) and temperature term in addition to the enthalpy. A reaction will be a spontaneous process at a certain temperature if the products have a lower Gibbs free energy (an exergonic reaction) even if the enthalpy of the products is higher. Entropy and enthalpy are different terms, so the change in entropic energy can overcome an opposite change in enthalpic energy and make an endothermic reaction favorable.