An increase adds stitches and creates shaping as a general rule. Lace patterns will use increases to balance decreases and you usually end the row with the same number of stitches you started with.
Many times, the pattern will tell you which specific increase to use; this is especially true with lace patterns. If the pattern tells you to simply increase, use the default increase: knit in the front and back of the same stitch (usually abbreviated kfb).
When working an increase in shaping, such as making sleeves wider, work them at least one stitch in from the edge. This makes seaming much easier.
Let’s take a look at some various ways to increase (click on any highlighted text to see diagrams:
As mentioned earlier, this is the default increase. It’s sometimes called a bar increase as it leaves a noticeable “bar” of yarn from the original stitch as it’s manipulated twice. It does not distort and it’s a perfectly fine increase except for the bar. If you don’t look closely, it will not be noticed.