Learn Italian: Quell'aeroporto è aperto oggi.

The word for "that" (quello) changes its ending to match the noun that follows it, acting exactly like the definite article (the word for "the"). Because aeroporto starts with a vowel, you use an apostrophe just like you would say l'aeroporto (the airport). So, quello becomes quell'.

How would I say "this airport" instead of "that airport"?

You would use questo (this). Just like quello, it drops its final vowel when the next word starts with a vowel, so "this airport" becomes quest'aeroporto.

Why does aperto end in -o?

Aperto means "open" and it acts as an adjective here. In Italian, adjectives must match the gender and amount (singular or plural) of the noun they describe. Since aeroporto is a masculine singular noun, aperto uses the masculine singular -o ending.

I notice an accent on è. Is it important?

Yes, it is very important! è with an accent means "is" (from the verb essere). Without the accent, e means "and".