Usually, votes are recorded, managed, counted and checked by a central authority. Blockchain voting empowers voters to do these tasks themselves, by allowing them to hold a copy of the voting record. The historic record could then not be changed because other voters would see that the record differs from theirs.
Illegitimate votes can not be added, because other voters are able to scrutinise whether votes were compatible with the rules (perhaps because they have already been counted, or are not associated with a valid voter record). Blockchain voting shifts power and trust away from central actors, such as electoral authorities, and foster the development of a tech-enabled community consensus.