In English, reflexive pronouns are a group of pronouns used for various grammatical purposes.
The easiest form of a sentence in English is the grammatical subject-verb-object construction, where the subject is also the agent, the thing doing the action. "He ate the apple". But for many English sentences, a standard SVO construction on longer is the most efficient way to communicate a thought. In English, three of the forms used in these situations are Passive Voice, reciprocal pronouns, and reflexive pronouns.
The simplest explanation for when a reflexive pronoun is used is when the subject and the object of a sentence are identical. We say "I gave it to myself" or "She told herself", because "I gave me" and "She told her" are not correct in English. This is actually a simple grammar rule, and the part of reflexive pronouns that fulfill their name. However, there are other uses of the reflexive pronouns that are of more ambiguous grammatical necessity.
In English, we use our reflexive pronouns as intensive pronouns. They are used to show that the designated person was the one responsible for the action, especially if it is against expectations. This usage is sometimes accompanied by the word "by". "No one else wanted to go to the beach that day, so she went there by herself" or "I made your birthday cake myself!" are both examples of this. Sometimes, when used as an intensive pronoun, the reflexive pronoun can go along with the subject: "Other people tell me it tastes bad, but I myself like hummus". This usage of the reflexive pronouns is natural for native speakers themselves, but is difficult to teach to non-native speakers.
While these two meanings may seem separate, there is a connection between them, which is that they emphasize the subject of the sentence as being more central than usual. And there are some sentences where the two meanings overlap. Especially when the reflexive pronoun is used with a normally intransitive verb: compare "He bathes every morning" with "Even after losing mobility, he bathes himself every morning". In the second sentence, the pronoun is both reflexive (the subject and the object are the same) and intensive (showing that someone is doing something, against expectations).
And like a great deal of English grammar, these two meanings lead to situations where a pronouns use as reflexive or intensive is ambiguous. "He asked who did it, so I told him myself" and "The mirror is broken, I saw myself" are both instances where the pronoun could be either.