Converged Infrastructure is one of those fuzzy but self-defining technology terms. Let's dissect the term.
Converge: "come from different directions and meet at (a place)" or "gradually change so as to become similar or develop something in common." (source: The Internet, unnamed)
Infrastructure: "The basic physical and organizational structures and facilities (e.g., buildings, roads, and power supplies) needed for the operation of a society or enterprise." (source: The Internet, unnamed)