this depends on weather u mean close as in end the conversation or close as sign out of the conversation site when your done but ill answer for the part of ending the conversation as the guy above already answered the other. Closing a conversation using more subtle tactics will help ease the transition from maintenance to end. Ending a conversation by referring to a future conversation might help a communication partner feel more satisfied with the conversation. For instance, "I'll give you a call tomorrow to continue this conversation" is better than "I'm tired of talking." During closing, we might let the partner know that we have been listening intently by summarizing the conversation: "Thanks for telling me about your experiences in the jungles of Ecuador." to put it simply its important cause it keeps your partner from wondering weather o not the conversation is over if u simply don't respond to messages as many people do they wonder if your done talking to them if they are blocked or even if you will ever talk again.