Agiganta comes from the word gigante (giant), and it means to make something grow larger or to intensify it. It's a vivid and somewhat dramatic verb that you don't encounter in every song.
In
Jessi Uribe's "Amor De Amante" is a passionate and a bit dramatic song about the pain of being the 'other person' in a relationship, or perhaps realizing the person you love has another lover. The singer is pleading, saying, "no me digas ni me mientas lo pido por favor" [don't tell me, don't lie to me, I beg you please]. Just looking at the person makes his pain grow, because he knows they have a lover.
He can't share his heart with anyone else and sees this whole situation as an "aventura absurda" [absurd adventure] for the other person. He predicts that soon they'll see it was all just an illusion. And when they come back, full of regret, it will be too late. The repeated line, "amor de amantes, el amor que estás tratando de vivir" [lover's love, the love you are trying to live], really drives home the feeling of frustration and heartbreak. It's a powerful song about unrequited love and the bitterness of betrayal.