A reaction is exothermic if ΔH (or [tex]\Delta H _\text{rxn}[/tex] in some textbooks) is negative:
A reaction is endothermic if ΔH is positive:
The enthalpy of a system is the sum of its internal energy. ΔH < 0 indicates that the reactants lose internal energy in the reaction. Energy conserves, and those internal energies must have converted to some other form of energy. They typically end up as thermal energy. The reaction will release heat since it is exothermic.
Similarly, ΔH > 0 indicates that the reactants gains internal energy in the reaction. Energy conserves. As a result, the reaction must have gained energy from its surroundings. The reaction will be endothermic since it absorbs heat.