A lattice is complete if all subsets have both a join and a meet. A complete lattice is more restrictive than a normal lattice.

Every non-empty finite lattice is complete.

Examples:

The power set of a given set, ordered by inclusion. The supremum is given by the union and the infimum by the intersection of subsets.

...

The convex subsets of a real or complex vector space, ordered by inclusion. The infimum is given by the intersection of convex sets and the supremum by the convex hull of the union.

References

https://en.wikipedia.org/wiki/Lattice_(order)#Completenes