Potenial form and できる
The potential form exists so that people can say that something "can be done". For godan verbs, the u is replaced with an e, then added る. So "u" -> "eru". For ichidan verbs, it is identical to the passive conjugation. Yes, that is confusing. It’s so confusing that sometimes you might come across sentences where it’s unclear/intentionally ambiguous whether or not an ichidan verb is used in passive or potential form. You just have to vibe with it.
食べられる (or 食べれる (!)) Can eat 殺せる Can kill 死ねる Can die 飲める Can drink
As you have probably noticed, 食べれる is listed as an acceptable variant of 食べられる with a big ! next to it. It’s common in spoken/colloquial Japanese to shorten ichidan verbs in potential form by removing the ら syllable (this is called ら抜き). It is not “proper” and should not be done in formal situations or in written form, but it is quite common in casual spoken language. It cannot be done with every ichidan verb, but there are no clear rules about which do or do not allow it. It’s up to personal preference, so don’t try to learn this rule. Just be aware it exists and learn to recognize it.
For the irregular verb する, we use the alternative verb できる as its potential variant. This is an exception, so it just needs to be learned as such.
昨日は勉強できなかった I could not study yesterday
To make the potential/passive duality even more confusing, we need to talk about a special quirk that potential verbs carry in Japanese that English does not have.
When it comes to potential forms, the notion of a “subject” and “object” in transitive verbs can become grammatically unclear. Let’s look at an example:
私はピザを食べる I eat pizza (not potential, standard form) 私はピザが食べられる 私にピザが食べられる 私はピザを食べられる I can eat pizza (potential, standard form)
What is going on here? All three of those options are valid and mean mostly the same thing. Also, depending on the context and surrounding phrases, the は in those examples can be が too (yes, you can even have 私がピザが食べられる, a double が sentence).
All you need to remember is that with potential verbs, が can be used to also mark the object of the action, not only the subject. And in those sentences, the subject can sometimes be marked by に. Some people consider the usage of を like in the example above to be improper, however it is incredibly subjective and you will see it so often that considering it improper is just for old men yelling at clouds. The を version tends to be more common in relative clauses or very long and complicated sentences.