Bermuda II is the bilateral agreement between the governments of the United States and United Kingdom. What it basically says is that any US or UK carrier can fly between any US airport and any UK airport except for Heathrow. In regards to Heathrow, it says that only two US Airlines and two British Airlines can fly US-LHR, but the flights to the US are limited to Boston, New York (includes EWR and JFK), Philadelphia, Washington (includes IAD and now BWI), Miami (I would think this might include FLL), Los Angeles, San Francisco, Seattle, and Chicago. Right now, the four lucky carriers are BA, VS, UA, and AA, but several airlines (Delta, Continental, Northwest, British Midland, and Virgin) want BII lifted and replaced with open-skies. Open-skies would allow any US or UK carrier to fly from LHR (or any other UK airport) to any airport in the United States. For example, LHR-ATL, LHR-DFW, LHR-DEN would come into place. The thing that is tying up Open Skies in part is the attempted AA-BA alliance. AA and BA want anti-trust immunity, but the US government has repeatedly said that they won't get it unless Heathrow is opened up to all carriers and that the new entrants (particularly the US carriers) are given sufficent slots at decent times, and these slots would be given up by AA and BA (BA is number one at LHR, AA is number three or four behind BMI and maybe VS).
There are several past topics on BII in the archive, just search that and you'll find enough information to keep you reading for a lifetime.