A constraint is a validation mechanism. It will guard that the data that you write adheres to your rules.
Your constraint CONSTRAINT SYS_STOREACCESS_UQ UNIQUE(USERNAME) will allow only unique values in column USERNAME. If your table STOREACCESS has a record with USERNAME == 'Joseph Sweet', and you try to insert a new record with USERNAME == 'Joseph Sweet', it will fail. Also updating another record to set USERNAME == 'Joseph Sweet' will fail.
Your constraint guarantees that USERNAME will only have unique values. No duplicates are allowed.