Chen (Mandarin 陈/陳) is one of Asia's great surnames. The main historical path is place-derived: people of the ancient State of Chen (in what is now Henan/Anhui) took the state's name as a clan surname. The character can also be glossed "to explain" or "old," but families usually inherit a lineage name, not a vocabulary quiz.
Romanizations vary: Chan (Cantonese), Tan (Hokkien), Vietnamese Trần, and others. US Census Chen is mostly Mandarin spelling; related forms may be filed separately. Type place (state name) fits best among the four buckets.