Ending a conversation can at times be hard. It is even harder if the conversation is occurring online and there is no way the other party can read your facial expression or body language. Since we have a society where being polite is necessary, you need to use twitter likes in case you are faced with such a situation. It is quite easy really. In the conversation, you would normally reply using the reply feature. If you want to end the conversation you could like their last reply instead of sending out your own reply.
This works such that, the other party becomes aware that you have seen their comment but are not going to reply. Since twitter is not all that private, twitter likes used in ending conversations is like saying, ‘I have to go, we’ll talk later’. You do not have to explain yourself as it would be inappropriate to disclose private information such as what you want to do while at the same time you are polite. It avoids being rude and you engage in a conversation with them later.