What are the functions of the callbacks in the commerce payment method info hook? Can someone explain me the differences, maybe with some examples, between the callbacks in the hook_commerce_payment_method_info()? 

The callbacks are these: settings_form, submit_form, submit_form_validate, submit_form_submit, redirect_form, redirect_form_validate, redirect_form_submit.

I'm trying to implement a payment module and I need to know how to use the callback of the above-mentioned hook.

Thanks
You can find Contributed Modules API Documentation in http://drupalcontrib.org/ portal.

Please find link to above hook documentation hook_commerce_payment_method_info .

Callbacks Documentation links below...

CALLBACK_commerce_payment_method_settings_form()
CALLBACK_commerce_payment_method_submit_form() 
CALLBACK_commerce_payment_method_submit_form_validate()
CALLBACK_commerce_payment_method_submit_form_submit() 
CALLBACK_commerce_payment_method_redirect_form()
CALLBACK_commerce_payment_method_redirect_form_validate()
CALLBACK_commerce_payment_method_redirect_form_submit()

Check out commerce_payment_example module to find out how to write a payment method for more information.