In order to separate atoms from one another you must break the bond that holds them. This requires energy, by definition a positive enthalpy change.
So if you break all of the bonds in the reactants you have the total positive enthalpy change of the reaction.
The opposite is true for bond formation. It releases energy and the enthalpy change is negative.
Hence to find the overall enthalpy change of the reaction is is the total enthalpy of bonds broken added to the total enthalpy of bonds formed, which is a negative value.
So the overall sum looks like:
total (bond enthalpy reactants) - total (bond enthalpy products)
As charco said above: if the educts are reacting to products, so make bond formations, energy is releasing and this is regarded with a negative sign. This kind of reaction is exothermic. If the products should react back to the educts, that would break the bonds, renergy is spending and this is regarded with a positive sign. This kind of reaction is endothermic.*