Do I understand it right?
Debian stable has stable versions of all programs/packages in its repositories and it is stable itself. Debian testing is another distro, so it is less stable itself and it is configured to download programs from another repositories. And those repositories contain the same programs as stable repositories do but testing repositories contain like beta-versions of all those programs (and just simply newer versions). And we can say the same about unstable branch.

In Debian stable we have
1. Stable Debian itself
2. All the programs in repository are also stable.

In Debian testing we have
1. Not that stable Debian itself
2. All the programs in repository are the same but less stable and newer. And this is another repository.

When some package has new version and this version it tested very good and found to be very stable, Debian community moves it to stable repository, overwrites the old version.

I just wanna make it 100% clear to me. Am I right?

Not quite. Debian stable is basically the latest "released" version (currently 5.0, codenamed "Lenny"). All the software was thoroughly tested on all of the different computer architectures Debian supports. When it was deemed that the number of bugs were low enough, it was released. Because of the amount of time to thoroughly test and the fact that releases only happen every couple of years, the packages tend to be slightly older versions. The repository of packages will only get security updates, no new versions of packages are released (though there is Debian backports repository where newer versions are made to work with the current stable release).

Testing and Unstable are different stages of developing the next stable release. New packages are submitted to unstable and are worked on and triaged until they work well. Then they migrate to testing, where they are tested more thoroughly. Eventually testing is "frozen" and Debian works to polish and test it into a rock solid stable release. Then things start migrating again from unstable to testing. So you can think of testing branch as a "rolling release" type distro. The packages are newer, but not bleeding edge. They're tested and bug fixed, but not "stable" by Debian's standards. Unstable is a rolling release bleeding edge distro.

Debian always has at least three releases in active maintenance: "stable", "testing" and "unstable".

stable

The "stable" distribution contains the latest officially released distribution of Debian.

This is the production release of Debian, the one which we primarily recommend using.

The current "stable" distribution of Debian GNU/Linux is version 5.0.4, codenamed lenny. It was released on January 30th, 2010.

testing

The "testing" distribution contains packages that haven't been accepted into a "stable" release yet, but they are in the queue for that. The main advantage of using this distribution is that it has more recent versions of software.

See the Debian FAQ for more information on what is "testing" and how it becomes "stable".

The current "testing" distribution is squeeze.

unstable

The "unstable" distribution is where active development of Debian occurs. Generally, this distribution is run by developers and those who like to live on the edge.

The "unstable" distribution is called sid.

sid will never be released. Packages go from sid into testing after a variable period of time, usually around 7 to 10 days.

Debian sid FAQ - http://wooledge.org/~greg/sidfaq.html

Debian - Wikipedia, the free encyclopedia - http://en.wikipedia.org/wiki/Debian

There is also Experimental, which is not a "release" like the others. Experimental is used for packages which are still being developed, and with a high risk of breaking your system. It's used by developers who'd like to study and test bleeding edge software. Users shouldn't be using packages from here, because they can be dangerous and harmful even for the most experienced people.

Once "stable" is released it does not receive new packages other than for security fixes and some bug fixes.

Don't be so obsessed with 'latest this or that.' Unless you know you need some feature way out there on the bleeding edge, it is probably more trouble than it is worth. Think about it this way...

Debian Stable: The least possible changes to packages you are using. This means no major version changes and lots of security fixes. This distro has strong package security tracking. If your main objective is uptime, and security, then stick with this distro. (later versions are found in backports!!!) If you are a sysadmin and like an uninterrupted sleep schedule, then run Stable.

Debian Testing: Versions change as the individual package maintainers feel necessary. The limits to changes are set mostly by when the distro maintainers call a freeze in preparation to a transition to stable. There is no effective security tracking like there is in Stable. That means holes can open/close. Bad bugs have been mostly resolved, but there might be some left. I have had no major surprises running Testing. Every once in a while an update won't work right. So, I wait a few days and then it is usually fixed. If you are a sysadmin and like getting woken up at night and the occasional customer complaint, then run Testing in Production.

Debian Unstable: Lots of changes to the very newest major versions of packages. So many changes that the repos and the applications themselves can break every once in a while. This is where bad bugs are found. If your Linux-fu is good, then running Unstable is not as scary as it sounds. If you want no social life and angry customers, then run Unstable in Production.

The average Ubuntu release is somewhere between Testing and Unstable in terms of reliability.

So if I use Debian stable, I won't have any program updates, that update versions? Only security fixes? And if I wanna have new versions of programs in stable Debian, I just should wait until new Debian stable (now it's v6) releases? It will have new versions of programs in its repositories?

Yes and no.
You can add the lenny-backports repository:
http://backports.org/dokuwiki/doku.php
It contains OpenOffice, gimp and other applications.

The new Debian-stable (which is now Debian-testing, called Squeeze)
will have got newer versions.
There will be a backport for Squeeze too.

From what i hear the actual Debian-testing (Squeeze) is stable enough.
Upgrading from Lenny(stable) to Squeeze(testing) might be a bit of fiddling. Squeeze itself seems quite stable.

If you ask me:
Install Debian-Lenny. Add the backports. Make up your mind. Either stick with stable/backports or upgrade to testing or re-install testing.
If you used any Debian-based distro (you say you use Mint, or Mepis, Sidux, Antix... whatever) you shouldn't have got much problems to find your way.

1. The 'new versions' may not be more useful to you. This is a common mistake. If you are looking for desktop eye candy, then newer is okay. If you are setting up reliable servers, then the latest hotness isn't your most reliable bet.
2. At this point in time, (May 2010) I would install Squeeze because it's very stable at this point. It'll go stable sooner rather than later.

No, I'm not. In fact, I don't like eye candy OS and programs, I like stability and graphics like is "OS/2 Warp". I am not an "eye-candy" user.