Something that happens with regularity is typical and expected. Fashion trends change with regularity, which is great for stores that want to sell you a new wardrobe every year.
Regularity is the quality of being stable and predictable. If you exercise with regularity, you might work out every day. If your car breaks down with regularity, then you're probably used to taking the bus. If you add the prefix ir- to this word, you get irregularity — something unusual, out of the ordinary, or unexpected.