Residual hearing is a term that is used within the deafness sector to refer to what a deaf person can hear. Very few deaf people hear nothing at all and so nearly all have some level of residual hearing. How useful this is varies from individual to individual. Some only hear some loud environmental sounds whilst others can hear some English speech sounds.
The best way to find out how much residual hearing your deaf student has is to ask him or her. S/he will be able to tell you what s/he can hear and how useful what is heard is to him or her.