The translation should be "the air is cleaner after rain". You can't have "a rain as rain is plural surely...?
rains has a slightly different meaning, it doesn't correspond to a plural form of "a rain" (which doesn't exist).
In English we would say "after the rain". "After a rain" is simply not possible in English. You could say "after a rain shower". Duolingo Owl, please help! Translation of "the" and "a" are so difficult from the Romanian - it can sometimes be a linguistic enigma!