Since none of the other replies actually answer your question, "serialized" means that the manga is being published in a magazine. Usually every time the magazine comes out, a new chapter of this manga will be in it. Most manga in Japan comes in this form. If a manga isn't popular, it gets cancelled, which is why a lot of manga series have abrupt endings (they get "axed"). It's also why a lot of manga has disappointing endings or lacks a cohesive story compared to a book.
"Serial" means "one at a time" and is used for all kinds of things. Examples include USB (Universal Serial Bus), which transmits data one bit at a time, or serial killers - people who commit multiple murders one at a time, like Jeffrey Dahlmer or Jack the Ripper. When a magazine or newspaper has a regular feature, you say that feature is "serialized."