"to sweep you off your feet" is to encounter a force that is so strong that it picks up your body (not literally but figuratively). So you might meet the "love of your life" and you are suddenly caught in a powerful emotion that you cannot control, you are given over to that love and .... etc

It's an idiom. The Spanish translation expresses the literal meaning but not the metaphorical use of "sweep" in the idiom. The Spanish translation omits the idea of suddenness and exhilaration that is part of the process of sweeping someone off their feet (or being swept off your feet). I like Bill's explanation - thumbs up. The same expression is also in "The way you make me feel", by Michael Jackson.

Normalmente esta frase significa que conquistar a alguien o hacer que ésta se enamore de ti. Puede ser porque eras guapo/guapa, le hablas bonita a la persona o cualquier otra cosa. Pero en esta canción se refiere a levantar a una persona. When your legs don't work like they used to before – Cuando tus piernas ya no funcionan como hacían And I can't sweep you off of your feet – Y no te puedo lavantar, alzar (en el aire)