If you're deaf, you can't hear or have extremely limited hearing abilities. Many people who are deaf communicate using sign language.
Some people are born deaf, while others lose their hearing later in life because of illness or injury. People who have been deaf their whole lives and are actively involved with the deaf community consider deafness a "difference in experience," not a disability. When someone accuses you of being "deaf to" their argument, they mean that you are refusing to pay attention or listen. Until the 18th century, deaf was pronounced so it rhymed with beef.