Tenouchi is translated as a grip. Let me explain the word a bit more though. "Te" means a hand. "No" means of. "Uchi" means inside.
So it is the inside of the hands.
Tenouchi is not something that is explained by writing easily but I will make it as easy as possible so that you can get some ideas about it.
When you are in chudan, your grip is not very tight. You should not have a very firm grip. Why?
That is because you have to tighten it up when you strike.
If your tenouchi is too loose, your opponent can knock your shinai off your hands.
Remember some exceptions.
The pinky and the ring finger of your left hand are always tight.
Basically you hold your shinai with these two fingers. The right grip, as always said, should be soft as if you were holding an raw egg. If you hold a raw egg tightly, you will break the egg.
That is how softly you should grab your shinai with the right hand.
Then when we should tighten up our grips?
At the moment that your shinai hits a target (men, kote, do or tsuki).
Only the moment. You do not want keep the grip tight. As soon as you hit the target, your tenouchi should be as relaxed as before you struck. Why?
Have you heard of Zanshin?
Zanshin is awareness or readiness, right? If you want to know about zanshin, you can go to an article "How Do We Apply Kendo Teachings in Daily Life?".
After your strike, you should be prepared for your opponent striking you back or ready to execute another strike on your opponent.
To do so, every bit of you, i.e. your body parts and mind, has to be back in the state before you executed a strike.
Thus, if you keep your grip as tight as you struck the target, then you are not in the state of zanshin at all. Besides, it is hard for you to execute another strike if your tenouchi is too tight.
If you drive a car, I think you do not hold the steering tightly all the time. I think you grab the steering tightly when you turn or when it is necessary; otherwise, your hands are pretty relaxed.
If you do not drive, try this.
Pick up something around you.
You do not grab it, whatever you have picked up, with the more strength than you actually need to hold it.
Your brain knows how much strength you need to pick it up and hold it still. Now move it and stop it and again move it around and stop it.
You need to grab it tighter when you change the course of the movement. And once you change the course of the movement, you feel that your hand and arm are relaxed.
This is how tenouchi should work too.
Your tenouchi should be very relaxed before you strike, but when you strike it should become very firm. Right after your strike, it should be relaxed again.
It sounds hard but it will come to you after thousands and thousands of striking practice. :)
* A piece of advice
Do not worry about HOW tenouchi should be.
When you do suburi (empty cut), try to stop your shinai without your kensaki bouncing. Try to stop your shinai at once. If you have too much strength, you see the kensaki of your shinai bouncing.
If you have a training partner, ask him or her if your strike is too hard. You do not hit your partner too hard. Your strikes should be sharp and fast but not as strong as you could destroy a rock.