Complex sentence: An ultrafilter may be considered as a finitely additive measure such that every subset of "X" is either considered "almost everything" (has measure 1) or "almost nothing" (has measure 0).
Split into simpler sentences: An ultrafilter may be considered as a finitely additive measure. In this view, every subset of "X" is either considered "almost everything" (has measure 1) or "almost nothing" (has measure 0).