Eructation is simply a fancier, and some might argue a more decorous, word for "belch." "Eructation" was borrowed from Latin in the 15th century; the verb eruct, meaning "to belch," followed in the late 16th century. Both have their source in the Latin verb eructare, which is the frequentative form of erugere, meaning "to belch or disgorge." (A frequentative form is one that denotes a repeated or recurrent action or state.) "Eructare" shares an ancestor with Greek word ereugesthai as well as Old English "rocettan," both of which also mean "to belch."
The poverty of most people's vocabularies these days is enough to make one belch in disgust.