Affordances, a term coined by James J. Gibson, are the relationship between the product and the user; the term refers to the properties offered by the product.
The specific affordance of the medium of text messages is that it provides additional medium of communication, especially when traditional means, like a telephone call, might be unavailable. Text messaging is a product that is perfect for people who need to communicate or need a quick response, so a further perceived affordance of text messaging would be the convenience of usage--being able to send a message without having to actually talk to the person.
Gibson, J. J. (1977). "The Theory of Affordances."