Does "clear of clouds" mean you cannot touch a cloud or does it mean that that Class B airspace must not have any clouds in it?
That specific phrasing means that you can't touch a cloud. See the VFR minimums in 14 CFR 91.155, where it says:
no person may operate an aircraft under VFR when the flight visibility is less, or at a distance from clouds that is less, than that prescribed for the corresponding altitude and class of airspace in the following table [...]
The table lists the "distance from clouds" in class B as "clear of clouds".
You can also find it in the AIM section 3-2-3 on class B airspace, and in other sections about SVFR, visual approaches etc. where a requirement for those procedures is to remain clear of clouds.
The actual cloud cover in the class B airspace is reported by METARs and ATIS.
It means that the pilot should not touch the clouds in VFR. From CFR 91.115: