A persuasive text is a text that really wants you to do something

An advert might want you to buy something.
You might write a letter to persuade a friend to go on holiday with you, or to try and get off a parking ticket.

Persuasive texts might use:

repeated words
text in capital letters
exclamation marks
rhetorical questions (questions where no answer is needed)
an emotional one-sided argument
humour

Examples:
SPECIAL OFFER! Buy today! Would you want to miss this SPECIAL offer? Phone NOW...

"I really think that you need this holiday. You have been working very hard lately and are so worn out. Just think of how nice it will be to lie on the beach in the sunshine."