Slander is technically speech that is both untrue and derogatory of another person, but my reading of this precept extends it to libel, or doing the same thing in writing. Again, the prima facie reading of this precept is an admonition against speaking poorly of other people, and like all the prima facie readings of these precepts, that's pretty good advice, but there's also a deeper and more subtle way to look at the issue here.
Deeper than that admonition is the reminder that once you come to the conclusion that your narrow view of another person's life contains sufficient wisdom to pronounce a judgment, i.e. to say something about another you do not actually know to be a fact (like something they intended, or believe--something in their mind), you have stepped off the path. That is, you've lost sight of what is really going on around you. You have foolishly decided that your own particular abstraction of reality can really support such conclusions, and further you've fooled yourself with the idea that there's really anything for anyone to gain from your interpretation of things that you don't, or can't, know to be true.
These are deeply deluded views, and since it is exceedingly difficult to rid one's self of all such nonsense, this precept serves to remind us that our lives will make more sense to the extent that any such notions are held very loosely, if at all.
Beyond this, a thoughtful examination of this precept reveals that the popular notion of a supernatural being who is both omniscient and disapproving, i.e., the common view of a God standing in judgment of mankind, is impossible. That is, if such a being could in fact know everything there is to know, then said being would never exercise disapproving judgment, because such judgment itself depends upon an abstracted and incomplete view of reality.
When you are seeing things as they really are, as an omniscient being would, you do so with the awareness that everything you see is perspective, not reality, and everything you hear (or think) is opinion, not fact. This is not to say that one can't have perspective and opinions, certainly we all do, but this precept reminds us that these perspectives and opinions are not facts. They are not reality, they are abstractions--a natural product of our mental struggle with a constantly changing and impermanent existence. In other words, it is one thing to say that something is wrong, and it is really quite another to say that you notice your own disapproval of something.
One can't know what is in another's mind. If you've decided that you know what someone else is thinking, you've confused opinion with fact. You can have an opinion about what someone else thinks, we all do, constantly. But, you can only know what you think. Even if someone verifies a guess you made about what they were thinking at some particular point in time, you still don't know if that actually was what they were actually thinking. You only know that they want you to believe you were correct. They are free to misrepresent their thoughts to another, just as you are.
It is important to know that being very, very confident that an opinion is accurate is not the same as knowing a fact. This is vitally important to making sense of the world.
One might be inclined to assert that God has better judgment than everyone else, or that God can read another's thoughts, so therefore God's judgment is okay, but that ignores the fact that judgment is still judgment. Judgment is not true seeing. True seeing does not judge, it simply sees. Flawed judgment isn't a matter of skill, the problem is judgment itself. Judgment involves walling-off from the wholeness of reality. It involves a conclusion that is de facto a limited abstraction. All speech is such.
So, for a being to be omniscient, this walling-off has to be seen-through. God has to know that any kind of thought like this, or any thought that can be expressed in words, is not the whole picture. Words can't be anything but an abstraction, including these words. So, one can be judgmental and speak, or one can be omniscient and aware. One can't be both.
Slander, that is, speech about another that is both untrue and disparaging, is always the product of some judgment. Relating facts, things that can actually be known (which excludes another's thoughts) doesn't involve judgment. Disparagemnt requires it. So, this precept serves to remind us that when we are inclined to speak in a way about someone else that does not involve the simple relation of actually known facts, and that speech is harmful and/or unkind, then we have become lost in this trap of delusion.
So, a follower of the way does not slander others.
Next - A follower of the Way does not praise self.