Are you referring to texts? I don't believe this is possible unless you had them backed up or saved somewhere. Your carrier might be able to assist you in some way getting a record of the messages, but I doubt that actually restoring them is an option.
I'm not sure how it's set up on your device, but on mine you can tap the menu at the top right in the messaging app and select trash. You can restore the messages from there, however, there is a limit to how long messages are kept before being permanently removed.