Correct spelling, explanation: this both countable and uncountable English word has its origin in Old French porpos, which evolved into the form we know today – purpose – in Middle English. The word functions as a common noun, but also as a verb in more formal contexts.

Definition of purpose:
1. noun – states the reason for something,
Could you tell me what’s the purpose of your rude behavior?
2. noun – a feeling that you do something meaningful,
The only thing that gives me a sense of purpose in my life is my work.
3. noun – a need,
I have difficulty finding a flat that suits my purposes.
4. verb (formal) – to have an intention,
He stopped loving her and even purposed to show it to the world.

Expressions with purpose:
1. on purpose – intentionally,
You broke my toy on purpose!
2. serve a purpose – to serve a good use,
A reliable bus network serves a really good purpose for the local people living here.
3. be to no purpose – to be useless and unsuccessful,
I spent hours preparing the dish, but it was to no purpose as my dog ate it!

Incorrect spelling, explanation: quite a common mistake among the users of English is to include a letter -o at the beginning of the word, which results in the incorrect form pourpose. It probably comes from the fact that we have a word pour in English, which has a similar pronunciation. In this case, however, it is wrong so pay attention to spell it correctly.