Yes, when a donor submits their donation they will see a confirmation message and they will receive a thank you email sent to the address they provided. You can customize the thank you message on the Thank You Message tab. If you allow recurring donations, you will see two thank you messages, one for the first donation and one for each subsequent recurring donation. You can edit these messages by clicking on the Edit Message button.
Note that if you are logged into AssociationSphere and you view the donation page and record a donation, instead of the confirmation message, you will see a message to reload the page. This allows you to enter multiple donations without needing to copy and paste the page URL to reload the page.