What does it mean if a functional group has "higher priority" in terms of IUPAC naming of organic compounds?
Whether trying to figure out if a double bond is "E" or "Z", or if a chiral center is "R" or "S", the Cahn–Ingold–Prelog priority rules (see the section "Assignment of priorities") are used to prioritize the groups.  In the case of a double bond there are 2 substituents (a lone pair of electrons can be a substituent) at each end of the double bond.  Priorities (1 and 2) are assigned to the substituents at each end using the Cahn–Ingold–Prelog rules provided in the link above.  The first rule used to set priorities is based on the atomic number of the atoms attached to the double bond.  If there is a tie (the 2 attached atoms at one end of the double bond have the same atomic number), then we move out to the next atoms and compare these.  The process is continued until the tie is broken (eventually the tie must be broken if the molecule being analyzed is really capable of being described as "E" or "Z").  After the priorities have been assigned, if the two priority-1 substituents at opposite ends of the double bond are on the same side of the double bond, then the molecule is the "Z" (zusammen, together) isomer, otherwise it is the "E" (entgegen, opposite) isomer.

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