Learn Italian: Un abbraccio forte per te.

Ti is a weak pronoun used directly next to a verb, like when saying ti vedo (I see you). But because this sentence has no verb and uses the preposition per (for), you must use a 'stressed' pronoun instead. The stressed form of ti is te, which is why we say per te.

Why does forte translate to 'big' here? Doesn't it mean 'strong'?

Yes, forte literally means 'strong'. In Italian, it is simply more natural to give 'a strong hug' (un abbraccio forte) rather than 'a big hug' (un abbraccio grande). English speakers say 'big hug', but the meaning is exactly the same!

Un abbraccio is masculine, so why does forte end in -e instead of -o?

Not all adjectives change between -o and -a. Words like forte (strong) or grande (big/large) belong to a group of adjectives that naturally end in -e in the dictionary. They keep this exact same -e ending for both masculine and feminine singular nouns.