Normal geocaches. If you go to the posted coordinates, you will find some type of box or container hidden there. Inside the container you will probably find a log book to sign and some trinkets to trade.
These are like traditionals except there are multiple stages. Clever huh? When you get to the posted coordinates you will find a container. However, there won't be a log book inside. Instead there will be anouther set of coordinates which lead to another box. That box might contain the log book or another set of coordinates instead. Eventually you will get to the final stage. Many multi-caches only have two stages, but some have many more.
For puzzle caches, you don’t want to go to the listed coordinates. Those coordinates will tell you the general location of the cache (within a mile or so). To get the exact position of the geocache, you're going to have to do some work. The cache description will explain how to figure out the actual coordinates. Sometimes it is a math problem or a logic puzzle. Other times you will be gathering historic information from around a park. Creative hiders have thought of all kinds of puzzles.
When you get there, don't be confused. With virtual caches, there isn't a container or logbook at the final location. Virtual caches are only allowed in places where physicial caches are prohibited or are otherwise unfeasible. But don’t let the lack of Tupperware concern you. Virtaul caches all have a search, seek, or do activity at the finial coordinates. Most have an educational, outdoor, or human interest component. Since there isn't a log book, some virtual caches will require you find a code phrase near the posted coordinates to log the cache. If a code phrase is required, it will be explained in the cache description.