from Okinawa Soba's Flickr photostream (CC)
Follow the link to see quite a few good kendo pics from more than 100 years ago.
溜める (tameru) means 'to build up' or 'to accumulate'. It is not mentioned in kendo as much as 残心 (zanshin) which as you know refers to the follow through after an attack, but the two are directly connected. You can't follow through without something to start you off in the first place.
So what is it actually?
The best description of tame (pronounced tum-eh) is to imagine you are like a bow. Your attack is the arrow. And your tame is the bow-string. If your tame is weak, it is as if you have not pulled the bow-string back very far and so the arrow will not fly very far. It will probably fail to reach the target. Your tame, your build up, must be like drawing the bow as far as it can go. The power is then almost too strong to hold, the bow vibrates with energy and the arrow strains to be released. As soon as there is an opening, your attack flies and there is no stopping it. When you think of it this way, zanshin is just a by-product of tame. And so it should be. Zanshin should not be artificial (such as forcing yourself to do extra footwork to pass your opponent), it should just be a natural part of the attack.
How do you develop tame?
There are two ways to develop tame. The first way is with kiai. When you kiai at your opponent, even before you have any idea of your first attack, the purpose is to build up your attacking spirit, in other words, tameru. You must always kiai strongly, and notice the effect it has on your opponent: did they kiai back? Did they flinch? What was their kiai like?
The second way is through attacking practice like uchikomigeiko and kakarigeiko. People who have trained regularly and hard, especially in these exercises, find it easier to have powerful tame. It is like they have found the tame switch in their body and in their kendo.