The collection of cofinite subsets of ℝ is a filter under inclusion: it includes the intersection of every pair of its members, and includes every superset of every cofinite set. Wiktionary

If (1) the universal set (here, the set of natural numbers) were called a "large" set, (2) the superset of any "large" set were also a "large" set, and (3) the intersection of a pair of "large" sets were also a "large" set, then the set of all "large" sets would form a filter. Wiktionary