As Peachy said, it is a Biblical term, and suggests that the hearer has chosen to ignore someone, not paying due attention to what is being said or taught. One of three instances fond in the Bible is in the gospel of Matthew 13:15, "For this people's heart is waxed gross, and their ears are dull of hearing, and their eyes they have closed; lest at any time they should see with their eyes, and hear with their ears, and should understand with their heart, and should be converted, and I should heal them."

No, it's not like "hard of hearing". You are/become dull of hearing. This means you are/become tired of listening and paying attention, and you don't want to listen anymore. This seems to be a biblical reference and sounds slightly poetic, so I wouldn't say it's a common phrase.