I could not tell you if I loved you the first moment I saw you, or if it was the second or third or fourth. But I remember the first moment I looked at you walking toward me and realized that somehow the rest of the world seemed to vanish when I was with you.

This quote is saying that although the speaker cannot pinpoint an exact moment when they fell in love with the person they are talking about, they remember the first time they saw them. At that moment, they felt like the rest of the world had disappeared and it was just them and the person they’re speaking about. This suggests the speaker feels a very strong connection with this person, which made them feel like nothing else mattered.