Definitions are to TERMS, the basic logical element (hence, ‘term’, is in ’terminus’ i.e. can’t go further), what Demonstrations are to Propositions.

Some propositions cannot be demonstrated BECAUSE they are TOO BASIC to ‘prove.’ Similarly, some things CANNOT BE DEFINED.
This is not a flaw in basic terms, that they cannot be defined, just as it is not a flaw in first principles that they cannot be demonstrated.
The reason that some terms cannot be defined should be obvious: we define terms by means of OTHER TERMS, and if there were no BASIC TERMS, then all definitions would be, eventually, CIRCULAR.

But circular definitions FAIL to define.
For example, Google’s dictionary (Oxford, not OED though) defines “sex” as “sexual activity.”

That is about as useless a “definition” as one can imagine.
For example, in physics, there are no real definitions of energy or matter.
Feynmann on energy.

Still true.
Plato in the Timaeus, or rather Timaeus is the Timaeus, speaks of a “bastard λόγος”—a kind of speaking that we use to speak about things we cannot properly speak about.
We don’t need to get into what Plato (or the Platonic Timaeus) designates “the χώρα”—but one can think of many cases where we run into, as Wittgenstein would say “the limits of language.”
An excellent example is … Nothing.

We have no concept of nothing, because nothing has no content for us to conceive. It has no properties. We cannot say “Nothing has property P” nor can we say “Nothing is.” Nothing does not exist.
And yet …

Parmenides says “Nothing IS NOT.”

And each of us has SOME IDEA about “nothing” or “the Nothing” as Heidegger calls it.
We all know that when Stephen Hawking equates “nothing” with GRAVITY + LAWS OF NATURE, or Lawrence Krauss equates “nothing” with QUANTUM FIELDS + LAWS OF NATURE — that these is wrong.

Nothing ISN’T either of those things, because they ARE something.
Nothing just is the isn’t.

That sentence both makes sense and remains baffling.

Much like Socrates’ assertion “The Good is beyond Being.”
“God” is obviously another of those things for which we cannot give a PROPER definition.

As is Being, Nothing, Existence, Essence, Substance.
We can give improper or to use Plato’s term “bastard” or “illegitimate” definitions.

STRICTLY, God cannot be defined.

This is my “bastard” definition of God.
This becomes ANNOYING when someone who doesn’t understand that not everything can be defined keeps demanding a definition of an undefinable term, and claiming that, if you can’t define it, you don’t know what you are talking about.
This is just as false as the claim that you don’t know that the first principles are true, because you can’t “prove” them, e.g. the law of noncontradiction.
You can’t “prove” the law of noncontradiction, because a proof would require terms which must BE something, not both A and ~A, and premise which must say “S is P” and not “S and ~ S is and is not P and ~P.” And a conclusion that follows, not one that does and does not follow.
Which is to say, “proof” is not as BASIC as the law of noncontradiction.

Discursive proof is “closer to home” in that humans make use of it a lot, but we do not notice that it depends on things SO BASIC we don’t even think to question them.

Unless we’re insane. Or philosophers.
Anyway, be aware that some things are TOO BASIC to be defined. That doesn’t mean we can’t talk about them, but it does mean we are going to have to redline what language is capable of.
Oh, and as an afterthought, OBVIOUSLY don’t do the 5-year-old’s iterated request for definition game:
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