A parenthesis is a word or a phrase that is inserted into a sentence to add information or explain something.
The extra information can be put inside commas, dashes or brackets.
My sister, who is called Emily, loves horses.
My sister - who is called Emily - loves horses.
My sister (who is called Emily) loves horses.
Brackets are used when the writer wants the information to stand out more than it would if commas were used. Dashes are generally used in informal writing such as emails.
The plural of parenthesis is parentheses, and the word is sometimes used to refer to the brackets themselves as well as to the information inside them.
The sentence should always make sense without the parenthesis, whether commas, dashes or brackets are used.