A biometric residence permit is an identification card that also shows your status as a resident of the United Kingdom. It's called biometric because it includes some information about your physical characteristics, namely your fingerprints and your digitally encoded photograph, encoded on an RFID chip.
This is similar to a biometric passport, and indeed the card bears the same "e-passport" symbol, as shown in https://www.gov.uk/government/uploads/system/uploads/attachment_data/file/261497/brp-information-leaflet.pdf.
I typed biometric residence permit into a search engine, and the first result it returned was https://www.gov.uk/biometric-residence-permits/need-brp. There, you can learn that the card includes
- your name, date and place of birth
- your fingerprints and a photo of your face (this is your biometric information)
- your immigration status and any conditions of your stay
- whether you can access public funds, eg benefits and health services