First in, first out (FIFO) means that the first thing that came in (oldest feed) goes out first. Every time you get new feed, you move all the old feed and put the new stuff behind it. Then you sell from the front of the pile (oldest feed.)
The other poster said LILO (last in last out), which would be pretty much the same (newest stuff came in last, and only gets sold after all the older stuff has been sold.) But I'm pretty sure that was a typo. They probably meant:
Last in, first out (LIFO) means the last thing that came in (newest feed) gets sold first, while the oldest feed sits in a corner and gets older and older. Every time you get new feed, you put it in the front of the pile and sell it first. The old feed may sit there for months or years, until one day there's a shortage of feed and someone finally pulls the old stuff out and sells it.
It's easier to just sell the newest stuff first, because you don't have to shuffle things around, so that's what people often do by default.
These terms apply to any situation where new stuff comes in and old stuff goes out. So it could be applied to a home refrigerator (put the new milk behind the old one, and finish drinking the old jug first) and to grocery store shelves (new cereal behind old cereal, new cans of soup behind older cans of soup), and to a deli as some people were mentioning above. I've even heard computer programmers using the same terms, when talking about how a computer handles & stores pieces of information.