There certainly are near-duplicate questions, but I'll take the opportunity to comment on the context of learning French as a second language since on is a common stumbling block.
First, on mainly has three possible meanings:
Nous, i.e. we, but more standard. In Canada, for example, you might hear politicians use on in debates and nous in prepared speeches.
On est prêt à sortir. Tu viens ?
The general they as in "They say you can hear it a mile away." (Or a general someone.)
On me dit que tu as obtenu un poste. C'est génial !
The general you as in "You want to switch gears at around 2,500 RPM."
Sometimes you'll see l'on. Same meaning, slightly more formal. A bit like saying "One ought to ..." in English.
On ne doit jamais mentir à un policier.
All these meanings are conjugated the same as il. That's why books that optimize the conjugation system omit it. It's the same reason your book omits elle, since that too is redundant with il.
From a grammar point of view, that's probably smart for a beginner. But outside of conjugation, it's obviously still essential to learn elle, and the same goes for on.
Teachers usually turn their attention to on later than nous (not to mention elle !), even though on is more common in actual speech. Students learning a language in a traditional grammar-focused way, like I did, might get to a high level before going out into the French-speaking world and wondering... What is this word people use instead of nous ?
There are a few reasons why it's taught that way:
On is less grammaticalized in the language, so it has certain difficulties and gaps for expressing some meanings. For example, it's easy to say "ourselves" with nous but not with on.
Much classic literature, and even slightly older literature that makes up the exercises and books schools can't afford to replace, uses the more formal nous, so there's more reading material.
Any pronoun that can have three different meanings will make translation confusing.
So for now it's probably a good idea to stick with nous when learning French as a second language. However, be aware of on in videos or when you practice speaking casually with friends.
In newer language-learning methods that are more focused on natural oral use, such as immersion in Canada, the teacher will use on very early in an attempt to mirror how native speakers learn it.
See the comments for further complications regarding this pronoun!
