Stitch holders are used to hold open stitches when not on a needle. These stitches will usually be replaced back onto a needle for further knitting. Often shoulder stitches are put onto a stitch holder, where later on the shoulders would be seamed together. When a piece needs to be split into sections, a stitch holder can securely hold those stitches for later use.
What size you need depends on how many stitches need to be moved to a stitch holder and how big the stitches are (such as fingering weight versus bulky weight).
Some stitch holders look like coilless safety pins, while some of the new styles more resemble a circular knitting needles. The latter is great when you have a large amount of stitches to hold. Plus, when you need to start working these stitches, you can knit them directly off the holder.