Promiscuous mode means telling an Ethernet card to record all packets that pass by, not just those addressed directly to it or broadcasts.
If that card is connected to a switch, however, then the switch normally only sends the card packets that are addressed directly to it (or to broadcast), so there's nothing else for the card to see.
I said normally because there are some circumstances where a switch sends other traffic out a particular port:
- the switch admin might configure it to do that (e.g. so an IDS can monitor traffic)
- the switch might do that if it is having problems (e.g. if it's not sure which port to send a packet to)
So you can't assume that just installing switches makes promiscuous mode go away completely as a threat; a determined attacker might attack the switch to try and make it do one of these things and send her host extra packets she can read with a promiscuous network card.
(And of course a determined attacked will do other things as well, such as attacking other bits of the network to make them send her packets they shouldn't.)
However, switches stop the casual user from using WireShark or Firesheep to poke about on the network; and in any case they offer other advantages, so most network managers have already upgraded to them.