Someone is pulling your leg. There's no such thing. You can't just walk into an office at the port and buy a cruise. Not anymore. Not since 9-11. Now the cruise lines need your name on a manifest so many hours before sailing so that the manifest can be made available to the office of Homeland Security.
However, that said ... there is something similar. Most of the cruise lines have "last minute cruiser lists" comprised mostly of people who live within driving distance of the major ports that they sail out of. These people are usually senior citizens who can be ready to sail with only a few days notice. When a cruise has a lot of empty cabins a week or two beforehand, the cruise lines will often start calling people on their lists and offering them cabins at cut-rate prices. The idea is to fill the empty cabins with warm bodies ... bodies that may make up for the cheap cabin rates by spending some money onboard. Since these people live near the port, they don't have to be concerned with hefty last minute airfares and so they can take advantage of these specials.
Be aware, though, that yes ... you will get some great deals ... but you will be taking the cabins that are left ... many of them being in what many consider to be "undesireable" locations. But, if you are not picky as to accommodations, it is true ... you can get some great last minute deals.
Just contact your favorite cruise lines and ask to be put on their last minute list. You may also want to contact some of the big travel agents in the area as well. Many times they are the ones who get the call to put together last minute groups for a block of cabins. I was on one sailing where a travel agent brought a group of something like 200 people onboard. They all had these special tee-shirts and I asked one of them about it. He told me that they only got the call to go on this cruise about two weeks ago and they got it for an unbelieveably low price. They were from a Leisuretown property about four hours from the pier, and HAL even threw in a bunch of busses to drive them to and from Fort Lauderdale. The TA threw in the tee-shirts and a bottle of wine for each cabin. Not a bad deal.
Blue skies ...