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I'm trying to get a deep understanding of the term: Density Altitude.

So I have read the explanations in my instruction book, and online articles.
One source explained it differently then the other which confused me.

Wikipedia defines Density Altitude as:

The density altitude is the altitude relative to standard atmospheric
conditions at which the air density would be equal to the indicated
air density at the place of observation. In other words, the density
altitude is the air density given as a height above mean sea level..".

https://en.wikipedia.org/wiki/Density_altitude

So if I would believe Wikipedia then I could look at the ISA table to find the altitude by using the pressure.

Here is an ISA table:

Let's say I'm looking at "22.22 Hg", then the Altitude would be 8000 ft.
The Density Altitude is also 8000 ft. Is this true?

Skybrary defines Density Altitude as:

Density altitude is pressure altitude corrected for temperature.

Link: https://www.skybrary.aero/index.php/Density_Altitude

This explanation contradicts with the other explanation:

the air density would be equal to the indicated air density at the
place of observation

So my question is actually: What is Density Altitude?
And is The Density Altitude with a pressure of "22.22 Hg" in combination with -0.9 °C equal to 8000 ft?

Try this article

https://www.aopa.org/training-and-safety/active-pilots/safety-and-technique/weather/density-altitude

As a pilot, we like higher Pressure and Cold Temperatures - it makes the air denser so the engine can create more horsepower. High Pressure systems, where the barometer reads above 29.92, and cold air, where the temperature is below 59F (I'm in the US) mean the aircraft will get off the ground sooner and climb better. So - Winter! Ideal flying time from a performance perspective.

Summer, we may see the same increased barometer reading, but the higher temperature means the air is less dense (heat makes the air expand), so engine performance suffers. Even worse, if there is a Low Pressure system, combined with high temperatures, can make the airplane feel like it is taking off from a higher altitude.

So Density Altitude is the altitude that the airplane thinks it is - the barometer reading with temperature impact added to it.

The concept of 'density altitude' is kind of like the concept of 'wind chill'.

Stick with me here, I'm going somewhere with this.

Cold weather is dangerous for the human body, and wind (because of increased heat loss on human skin) makes it worse. But how much worse? Is it worse to be outside in -10C temperatures with a 20 knot wind, or -15C temperatures with a 12 knot wind? The concept of 'wind chill' resolves those two values into a single easy number.

Density altitude works the same way. It's difficult and tedious to compare and contrast how an airplane will perform on a 25C day with a pressure of 29.80 at an elevation of 600 MSL, versus a 20C day with a pressure of 30.17 at an elevation of 1250 MSL. We need a way to mash all of these variables into one easy-to-use number. That number is density altitude.

So just as I can say "The wind chill is -10C" and it doesn't matter whether it's warm but windy or cold and calm, I can say "The density altitude is 2,000" and everyone will have the same idea of the expected performance of the airplane, no matter what combination of factors led to that result.

Once you start thinking of (and using!) density altitude as a simplification tool, its value becomes a lot more obvious.

Suppose you are at a given place, with a given temperature, and the barometer shows –for example– 25.84 inches of air pressure. That's precisely the pressure at 4000 ft. altitude within the 'standard atmosphere'. Hence, you may say that the 'density altitude' at that place where you are is exactly 4000 ft.

Density Altitude, in a nutshell, tells you how the plane is going to perform, in particular the climb performance for takeoffs or go-arounds.

The performance tables in your POH are based on ISA, which for practical purposes no plane ever actually flies in. That means you have to calculate the density altitude for the current conditions and look at that line in the tables to find out what the actual performance will be.

If the density altitude is very high (i.e. approaching your service ceiling), it's possible that your plane won't be able to clear obstacles/terrain or, in extreme cases, even get off the runway. This happens frequently to non-turbo pistons in mountains in the summer, and it is occasionally bad enough that even airliners can't take off from airports like PHX and LAS.

Any time your planned flight will be High, Hot and Heavy (known as the three H's), you need to consider DA and check the performance tables to determine whether it will be safe. High terrain may mean a different route via mountain passes; Heavy load may mean ditching passengers/cargo or fuel, and Hot may mean waiting until night or early morning. If any of these aren't things you encounter regularly, e.g. because you live in a (relatively) cold and flat region, it would be wise to check with a CFI to refresh your knowledge and double-check your plans before you go.

This is a classic video that explains it all:
Density Altitude