Have you ever been in a situation where someone is talking to another person so loudly that other people are also following the conversation? The person talking is usually not aware of this. I have seen this happen many times in very common places e.g. at the dinner table, on the bus, etc.
If the person suddenly recognizes that other people are “tuned in to the conversation” there is usually a moment of self-awareness followed by embarrassment. This is a good example of a lack of awareness of oneself. There are many other examples where people are unaware of their own being. It can easily be avoided by being tuned into your own environment and being conscious of your own actions