What this implies for our culture is not entirely clear yet. In the past communication was by long winded conversations and telephone calls. Of course in many circumstances throughout history a short message was enough to convey all of the necessary information (example: "the British are coming!") although those circumstances did not seem to pervade society in the way that texting is invading life now. With more ways that ever before to stay in contact with people we often feel that we have shallow relationships. It is like we are alone in a crowd. Technology is for us to use, but we are not supposed to be used by technology.
Conversations can be carried out with exchanges of these short messages but I think their real power is either to ask and answer a single question or just to provide a piece of information. When there starts to be multiple questions and large pieces of information other forms of communication are more practical. It is a skill to be able to send short messages well. It must convey all the information and still make sense. A message with too many questions or made up abbreviations is not effective.
Do not run away from short text messages, but use them to save time and say what you need or just what you want; however, keep in mind there are other forms of communication which can be more effective and can save time, confusion, and even money depending on the situation.