It's the 3rd singular person of the verb "mancare", that mainly means that something is missing, but it has also other meanings. Examples: I miss you = mi manchi, manco di esperienza = I'm lacking experience
I screwed up the listening exercise, and now I am wondering if "Manca un mese hai campionati" is a valid Italian sentence meaning "there is one month until you (have/do/hold/participate in) the championships"?
it's "manca un mese AI campionati". Ai is a preposizione articolata (preposition + article) So we have "a + i" = ai = "to the"
The problem is that you then have two main verbs, so you'd have to interpret it as two separate phrases: "manca un mese; hai campionati", which would translate to "there's a month to go; you have championships". I suspect that "hai campionati" is not very natural Italian, though.