What do the zeros in parenthesis mean in guitar tabbing?

http://www.ultimate-guitar.com/tabs/d/de...

Parentheses around a fret number, like this "(4)" mean either the note is optional (it isn't played every time) or it is a "ghost" note, one that is not struck but rings anyway.

In that "Layla" tab it looks like the notes in ( ) are simply ringing / held over until the next strong downbeat. Ordinarily parentheses can represent ghosted notes or artificial harmonic notation such as 14(2) -- push down the second fret and tap at the 14th fret.

open strings

its to help you keep time. He's pretty much saying the last note from the measure before is still ringing out and you dont start the next note at the beggining of the next measure, its a little thing called phrasing.

It indicates the open strings.