To reclaim something is to get it back. If a divorced couple remarries, they reclaim their marriage.
To claim is to declare or take ownership of something. To reclaim is to retake something lost. An injured quarterback must reclaim the starting position from his replacement. Two countries fighting over territory may lose and reclaim an area of land. A bank can reclaim a house if you don't make mortgage payments. Reclaim comes from the Old French reclamer, "to call back," which is rooted in the Latin word reclamare, "cry out against, or appeal."