The "burner" phone is a cheap handset that use pre-paid SIMs which can't be traced to the actual user. After they are no longer needed, the burners are destroyed and discarded. By demanding ID before allowing the purchase of a mobile phone, officials believe that they can make it more difficult for terrorists to communicate with each other.
On a Facebook page introducing the proposal, the Congresswoman says, "This bill would close one of the most significant gaps in our ability to track and prevent acts of terror, drug trafficking, and modern-day slavery." This issue is different than the one about encryption. Law enforcement officials are hoping to force phone manufacturers to add a backdoor on all handsets so that the authorities can figure out what the bad guys are up to.
Would it bother you to have to present personal ID when purchasing your next smartphone? Or is a little inconvenience worth it to stay protected from the evil in this world.