To root for means to support or hope for the success of a person or group, entering a contest, or undertaking a challenge.

For example:

In every World Cup, we all root for Brazil. There’s no better, undoubtedly.

I’m sure you’ll win. Everyone’s rooting for you.

The room exploded with shouts and cheers as people rooted for their favorite team.

His whole hometown was rooting for him as he made his professional boxing debut on live television.

Are you rooting for anyone in particular, 

or are you just shouting because you’re excited? I’m rooting for the home team.

Tradução:

Root for é um phrasal verb (verbo frasal) que significa “torcer por” algo ou alguém, como um time, uma causa etc.