How To Make Your "Incomprehensible" Beings Comprehensible - And Why You Need To

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Most "incomprehensible" beings can easily be made comprehensible by answering the following:
1. What is it trying to accomplish?
2. What does it hope to gain from accomplishing that?
3. What pleasure, advantage, or advancement is this gain supposed to bring?

For example: A space monster is trying to destroy the planet. It hopes to gain points in a cosmic space monster game. These points will give the monster satisfaction and bring it closer to beating the other space monsters, which will bring more satisfaction.

Is your being doing something that is normally considered abhorrent by human standards? You can add a fourth question to the above:
4: What is the reason it does not perceive this action as wrong or disgusting?

For example: Humans and human life have no real relevance to the space monster. It regards humans as a human might regard an unusual stain on the kitchen counter: it's mildly interesting, but you're still going to wipe it off because you'd rather have lunch than have an unusual stain. This monster would much rather have the points because if it falls behind in the game, it will face mockery from its peers and won't gain the satisfaction of winning.

Or is it having an emotional reaction? Then you answer the following:
1. What is it feeling right now that made it act out this way?
2. What happened to produce that feeling?

For example: The faerie queen is feeling extreme anger due to a severe negative emotional response in reaction to the sound of human voices.

If your beastie's actions are driven by instinct or similar, it can still be made comprehensible by answering a few questions:
1. What is it being driven to do?
2. What is the cause of this drive?
3. What purpose is this action supposed to serve?

For example: An animal is being driven to mate. The cause is seasonal cues triggering the production of hormones that produce an urge to mate. The purpose is to make more of itself, as all self-replicating organisms do or die out.

Is it some kind of machination or construct? You can answer this:
1. What was it created to do?
2. Why did someone want it to do that?

For example: An ancient AI was created to defend a city against intruders. Its creator wanted to keep the city safe.

Is it naturally-occurring, IE, formed without any conscious intervention?
1. What forces in the universe acted or came together to produce this?
2. What forces are acting or interacting to make it do that?

For example: The mindless gibbering mass of tentacles was formed because energy created by everyone's repressed desires coalesced and took physical form. It's twitching like that because its barely-formed brain is shooting off electrical impulses that make its muscles convulse.

And your being's true form can be easily addressed by answering two questions:
1. If someone was to look at it, what would this person see, hear, smell, etc.?
2. If that is not the entirety of this being, what is the rest of it like?

For example: A human being looking at this would see a figure which imitates but does not quite capture the appearance of a human - it has an appearance that might be described as scarecrow or rag doll-like. This figure is actually a projection or extension of the creature, sort of like the lure of an angler fish. The rest of the creature is something like an inky black mass that inhabits extradimensional space, though it sometimes comes into our dimension - which is why everything seems to leak black goo whenever the humanoid figure is around.

If you fail to answer these questions and keep on insisting that your creature is just too far beyond human imagination to comprehend in any way, shape, or form, what you're essentially doing is placing a cup upside-down on the table, then insisting there's something utterly mind-blowing beneath it and that nobody can even begin to fathom what it is. While it might be true that people really have no idea what's under the cup, it doesn't change the fact that you're trying to make people scared of an empty cup. And far too many people essentially end up trying to impress or scare people with empty cups. Some do take things a step farther and make the effort of slipping a bit of tentacle underneath of it. Then they lift the cup up enough for people to see the tentacle - and insist that it belongs to a horrifying monster they can't fathom. But of course it doesn't; the only thing under that cup is a piece of seafood.

Figuring out what your own creature is like and what it's about won't diminish your ability to make it creepy at all, because being creepy is more about what you do than what you are. Neither does it diminish your ability to make it mysterious for pretty much the same reason.

Again, you don't necessarily have to reveal the answers to these questions in your story, but to flat-out declare that something is and forever will be beyond the grasp of human imagination is to either insult the scope of your readers' imaginations, or to admit the limitations of your own.