A person who is self-important thinks that their thoughts, opinions, or actions are more important than anyone else's because they are better than everyone else. You can also use self-important to refer to things that a self-important person does. This word is disapproving.
examples:
The room was filled with self-important politicians.
He was known for his self-important yet boring lectures.
Superior is similar to self-important, but is used only of people and their characteristics, not the things those people do. It is also disapproving.
Example:
Her superior and smug manner made conversation unbearable.
I can't stand him - he acts so superior to the rest of us.
Someone who is conceited thinks that they are the best
Example:
He's so conceited and self-centered, he thinks no one can understand his genius.
Not to be conceited or anything, but my cake is the best cake ever.