Why might a network interface (NIC) be in "promiscuous mode" and what does it mean?

Issue

• Need to know the meaning of the following messages:

  Feb 24 12:15:14 server kernel: device eth0 entered promiscuous mode
  Feb 24 12:15:39 server kernel: device eth0 left promiscuous mode
  

• My NIC card has the PROMISC flag set in ip and ifconfig output:

  # ip link show eth0
  2: eth0: <BROADCAST,MULTICAST,PROMISC,UP,LOWER_UP> mtu 1500 qdisc pfifo_fast qlen 1000
      link/ether 52:54:00:4b:72:87 brd ff:ff:ff:ff:ff:ff
  

• Hundreds of messages device ethX left promiscuous mode

• How to avoid the promiscuous mode messages being logged repeatedly?