If you are single AND a full-time student you are exempt from paying council tax. The discount applies where full council tax is based on 2 or more people in a household, what the council site is explaining that if someone in your household is a student/student nurse, i.e one person, then the other person(S) (should they not come under the list for exemption) qualify for a discount (usually 25%). In this lady's case as she is single she currently qualifies for 25% discount but if she starts a full-time course, she will therefore be classed as a student and as the only adult in the household will not pay council tax.
Hope that helps, not sure if I've explained it as clearly as I could have!