The thing is I did my internship with the second company last summer. They know me there already.
Honestly speaking, I accepted the first offer as a safety net. But after I accepted the offer, I did not even bother to look for other jobs. But now this place, where I did my summer internship, asks me if I want to come back and wants to give me better offer.

The second company knows that I have the offer from the first company.