The phrase "unlimited messages" means that there is no restriction or limit on the number of messages you can send. You can send as many messages as you want without any limitations.
You can send / receive unlimited messages for free. (fsat.ru)
Our app features the fastest growing active database of christian singles where users can send and receive unlimited messages for all the christian singles on our app. (fsat.ru)
This is a completely free dating network with unlimited messaging for all singles who sign up. (datingadvice.com)