Reflexive pronoun conveys its meaning in its name as well as reflexive verb. It "returns" action or indicates the subject which we are talking about.
Я всегда уверен в себе и доволен собой - I'm always confident in and content with myself.
На выборах кандидат долго говорил о себе и своей программе - A candidate spoke about himself and his program a lot in an election.
As the last example shows, reflexive pronouns can be presented as with the word "себя" [sibya] - himself (indicates a person whom we are talking about) as with the word "свой" [svoy] - his (indicates the belonging of an object to a subject). Reflexive pronouns are changed only in objective cases, i.e. if we are talking about subjects that are belonged to different categories of gender (e.g. feminine and masculine) or change their number (singular or plural), the pronoun "себе" [sibe] is not changed depending on gender and number.
Он купил себе мороженое - He bought himself ice-cream.
Она купила себе мороженое - She bought herself ice-cream.
Они купили себе мороженое - They bought themselves ice-cream.
The pronoun "себе" is declined in cases (but it doesn't have root form, i.e. the form of nominative case).
Делать для себя, возвращаться к себе, хвалить себя, брать с собой, думать о себе - Do for myself, come back to myself, praise myself, take with myself, think about myself.
In this case only related word will be changed.
Самой себе [samoy sibe], самому себе [samamu sibe], самих себя [samikh sibya].
We often use reflexive pronouns in idioms and colloquial expressions.
Ничего себе (espression of amazement) - Oh Boy.
Так себе (expression which means «не очень нравится» - don't like it so much, «не впечатляет» - it doesn't impress me) - not up to much.
Не в себе (bad mood, feeling sick) - of a bad skin.
Сам по себе (independent, private) - by oneself.
Хорош собой (attractive, handsome) - good looking.