One extra point is conversation flow, a natural-sounding conversation is like a theatre play with a beginning, climax, and end. Think of it as improv with actors on stage. A nice conversation requires both speakers to understand this flow. This is why diplomatic talks have a slight rhythm to it if you can spot it. Transitions and reply length all factor in, sudden changes in topics, giving a short curt answer after the other speaks at length, the abrupt ending of the conversation, all of these can break the flow and come across as rigid.
Even then differing social status and power dynamics also affect the pacing of the conversation. A superior tend to speak more and if a subordinate speaks at length as well, it can either come across as insubordinate or a show of trust by the superior. These also vary from culture to culture with varying effects. Sometimes just giving a long reply regardless of what is said can be a sign of the power dynamics.
Then there is tone, it depends on who you are speaking to and in what context. That determines the language used from a "yeah sure" to an "of course" using the wrong wording can come across as poor communication skills.
If you want an example of all of this, take for example this context:
A King passes a decree, all of his retainers reply in short sentences with formal speech-like.
"Of course your majesty"
"We will carry out your will post haste."
But when they leave his most trusted advisor speaks to him in a very different manner. He speaks less formally and in much longer sentences. Telling the king this is a bad idea and why. The fact that the advisor is able to do this implies trust between him and the king and the advisor understanding that he can speak to the king like this is also a testament to his communication skills.
Understanding how to say it, how much to say, and when to say it is crucial technical aspects of good communication. Listening, understanding and empathy are important as said in other comments but one cannot also discount the technical aspects of it. There are of course exceptions to this rule, knowing when to break these rules is also a sign of good communication skills. A usually obedient subordinate suddenly speaking out of turn in a time of crisis and knowing when is a good time to do this is also a sign of good communication skills.
In essence, these are basic rules but the trick is knowing when to follow them, when to alter them and when to break them.
