Arbaeen means fortieth, and it marks 40 days since the anniversary of the martyrdom of Imam Hossein (PBUH), the third Shia Imam, in the Battle of Karbala in 680 AD.
Imam Hossein and 72 of his companions were martyred on the 10th day of the month of Muharram on the Islamic calendar. That latter day is known as Ashura. And Arbaeen marks 40 days since that day.