Swing is a feel, and there is no real way to notate it perfectly accurately. You can think about it as a delay on subdivisions, usually eighths. Or you could think about it as an anticipation of the quarter.
Normal 2 eighth notes are equally "spaced" from each other. When it's swung the first eighth takes more, so maybe 55% - 70% of the length of the quarter, and the second eighth takes the rest. The heavier the swing the more time the first eighth takes.
Some people think about it (and it's sometimes notated) as eighth note triplets where the first two triplets are tied, but thats not exactly right either.

According to my rough calculations, the position of that eighth note that determines the amount of swing can be inside a range of time slighty shorter than 0,1 seconds for a tempo of 120 Bpm: that's the reason why it's extremely difficult to tell 35% from 78% or 66%...
Let me share this graphic I made a few days ago when I realised I will get no further on Swingbeat:

Patrick Parlardy's and Cuantasvacas' posts describe 8th-note swing. I'm going to describe 16th-note swing(as SoundGym's SwingBeat game uses - exclusively) with a screenshot of Logic Pro’s list editor where I’ve made a bar’s worth of straight (no swing) 16th-note hi-hat notes on every 16th note in the bar.
Then I applied ‘1/16 Swing F’ quantization to the just second half of the notes in the bar (beats 3 and 4), for illustration ( a normal swing beat would have all four beats with swing, not just the last two.) In the screenshot, in the Position column, see how the syncopated beats for beats 3 and 4 have tick values of 101 instead of 1. So those hi-hat notes will sound later than straight 16ths - that’s what gives it the swing feel. {EDIT: for those unfamiliar, in the screenshot, the Position area's four columns of numbers are, from left to right: Measure/Bar | quarter note | 16th note | tick (960 per quarter note) }
Note ‘1/16 Swing F’ is the heaviest swing quantization in Logic Pro, and I’m going to guess that is pretty close to the what Sound Gym’s SwingBeat game calls 100% swing.
The other Logic Pro 16th note swing quantization options are these and what the syncopated 16th-note tick values would be in the List Editor, from light swing (1/16 Swing B) to heavy swing (1/16 Swing F):

1/16 Swing A - 1 (no swing)
1/16 Swing B - 21
1/16 Swing C - 41
1/16 Swing D - 61
1/16 Swing E - 81
1/16 Swing F - 101
So in SwingBeat, you’re just guessing the degree of swing from light to heavy (from 0% to 100%, respectively).

Another way to understand 16th-note swing is thinking of all 16th notes counted like this (for four bars): " 1 ee and uh 2 ee and uh 3 ee and uh 4 ee and uh". In a straight rhythm, all those counts are equally apart in time from each other. In a swing rhythm, the 'ee''s and the 'uh's are counted later than the straight beat to give the rhythm a swing feel.

The thing is I feel it's pretty pointless to develop such a superhuman skill. I believe in the importance of beeing able to tell swing from straight, maybe even certain degrees of swing (light, medium, hard), but a percentage?? I reached Swingbeat level 35 last week and I'm not physically able to improve anymore. Apart from 0-20% and 80-100%, depending on the rhythm pattern and speed, the rest is pure guessing/good luck...

I think the levels should start off with slower tempos and graduate to faster ones. I also quit playing SwingBeat because I didn't see the point.

thx a lot every one for the realy great explanations! :) (even with screenshots, really nice!! :D)
If I understand it correctly it's in short just a small time variation on 8th and 16th (and maybe also 4th?) note.
The resaon that I'm asking it is also because I'm really a beginner in making music and I try some times to expirment with swing, but I''m always ending up disabling it because it sounds so artificial to me.
so one last question, do you guys use swing sometimes in your songs? :)
and also do you know songs your really like, that use swing? :)
thx again for the really great explanations!!! :D