The problem here is that every time someone is infected with the virus, millions of copies of the virus are produced in their bodies. Each time a copy is made there is a chance that a mutation (a copying error) will occur. Each time a mutation occurs, there is a chance a new, more deadly version of the virus will result, possibly one with which the current vaccines can't help.
Vaccination "revs up" your immune system to more quickly recognize and start destroying virus particles when they invade your body and are produced by your cells. The result is fewer copies are made = fewer mutations = lower chance of a new, more deadly variant for which the current vaccines don't work. It also means you become less sick.
So there are two reasons to get vaccinated: to get less sick if you are infected and to help protect everyone from a new variant of the virus arising.