This is the remainder when 8 + 13 is divided by 6. If you need to find out what a remainder is, see, e.g., here.
Another way of thinking about this is 8+ 13= (6+ 2)+ (6+ 6+ 1)= 6+ 6+ 6+ 3= 3 (modulo 6) since "modulo 6" means that we "throw out" sixes. emakarov's point was that we can first add 8+ 13= 21, then divide by 6: 6 divides into 21 three times with remainder 3 so 21= 3 (modulo 6). You could also "reduce modulo 6" before adding: 6 divides into 9 once with remainder 2: 8= 2 (modulo 6). 6 divides into 13 twice with remainder 1: 13= 1 (modulo 6). So 8+ 13 (modulo 6) is the same as 2+ 1 (modulo 6). 2+ 1 = 3 which is less than 6 so 3= 3 (modulo 6).