1. To demand as one's own or one's due: Harriet was claiming that she should inherit the valuable jewels from her aunt even though she was not the legal heir to the fortune.
2. To make an application for indemnity; especially, from an insurance company: Jason claimed a substantial compensation for the fire that destroyed his house when the electrical system broke down.
3. To assert or affirm one's possession of something special: Jimmy and Tommy each claimed that the last piece of cake was his.