"One" is used as a pronoun, in place of "a person". While it's true (as Mick says) that it's not as commonly used these days I think your English is advanced enough you should become familiar with it. It can be a useful genderless pronoun if you don't want to pick between male or female.
"One" can be used in place of "you", for example:
One should take care not to use "one" too frequently, lest one sound pompous.
It can be a little tricky to use "one" in a sentence. It can seem overly formal to use "one" too many times in a sentence, but at the same time it can be awkward to switch between pronouns, especially if you're trying to avoid gender. Example:
"One needs to provide food for oneself and one's family". (formal)
"One needs to provide food for himself and his family." (less formal, but requires you to pick between the male and female pronouns)
"One" is a third-person pronoun, so it can be useful if you want to avoid saying something that could be interpreted as directed at the listener.
"You need to provide food for yourself and your family" (fine, but the listener might think you're talking specifically about them)
"One" also doesn't work well as the object of a sentence:
"I give one an apple" (formal, but sounds very awkward)
As you noticed, you can use the possessive "one's" and the reflexive "oneself". As before, these are formal and should be used carefully, once you understand the nuance.
Lastly, "one" is much more common in writing than when speaking, and you should probably avoid it in conversation as it can sound awkwardly formal.
More information on using "one"