Teatro literally means "theater" or "playhouse." While it's a common word, its use in this song is particularly interesting and metaphorical.
In "El Gran Teatro," Santiago Cruz uses it to describe a facade or a pretense. The phrase "que siga el gran teatro" (let the great theater continue) refers to the act of pretending that a past relationship is over and forgotten, even though the feelings still linger. It highlights the dramatic irony of the situation, where the ex-lover is putting on a show of happiness for others, while secretly still thinking about the singer.
Have you ever felt like someone was putting on a show for the world, but you knew their real feelings? In "El Gran Teatro," the singer addresses a former lover who seems happy in a new relationship. Everyone says she's smiling, but the singer knows it's all an act, a "grand theater."
He knows her secret: she still cries for him when she's alone and thinks about him constantly. He tells her not to worry, he won't tell anyone that she hasn't forgotten him. He then challenges her to lie to her new partner, daring her to say that she's never felt a love so intense before. The singer is confident she can't, because he knows he's still on her mind.