Increases are a common feature of a lot of patterns, both those worked in the round and those worked in rows, such as crocheted garments. It’s how a tiny little ring of 6 or 8 (or however many!) stitches becomes a whole blanket! When written in pattern terms it is often written as 2(stitch type) into next stitch. E.g. 2tr into next stitch. All it literally means is make two of that stitch into the next stitch. In rounds you normally make an increase in every stitch in the second round, then every other stitch in the third round, then every third stitch in the fourth round and so on (if the intention is to make a flat, round piece). Sometimes when creating ruffles you might make more than 2 stitches into one, but the principle is still the same. In crochet squares the increases tend to only be made at the corners after the first couple of rounds (this varies by pattern though).
When increasing on pieces worked in rows it still works in the same way, but obviously the pattern of increases will vary depending on what you are making.
In case you were wondering, decreases work on a similar idea, but turn two stitches into one. Basically you make 1 stitch up to the last stage of completing it (2 loops left for Double and treble crochet, 3 for half treble), then make another into the next stitch up to the last stage, then pull through all of the stitches on the hook. My post on clusters also explains the process in more detail.
Short but sweet post from me tonight, hope it’s helpful if you’ve been wondering about increases (and decreases).
Have you ever used increases for anything other than basic squares or circles? My favourite so far has been the tentacles on my jellyfish in A is for Amigurimi where I made 2 stitches into every chain of my foundation chain to make them all twisty.