Well, it's pretty easy with the right background. Just like chess, you can kind of 'stack' knowledge. You don't forget everything you learn (in fact, you forget very little of what you learn if you study regularly) so things that used to seem hard begin to seem easy and you can tackle more difficult stuff.
I'm not sure if you copied it wrong, or if the person just doesn't know what they are talking about, but there are a few things wrong with your sample sentence. First of all, there is no such thing as a 'minor fifth.' Also, the 7th and 4th notes of a scale are the 3rd and 7th of that scale's dominant 7 chord.
Basically, what they are trying to say is that one of the most commonly used ways to create tension and resolution between chords is to resolve the dissonant sounding tritone (or augmented fourth or diminished fifth) in a leading tone chord or dominant seven chord to the very consonant sounding major third interval in the tonic chord.
The 'dominant' chord is the chord built on top of the fifth tone in the key's scale. So, say we are in the key of C major. The dominant chord will be G major. This will consist of the notes G, B, and D. The dominant seven chord will include the added seventh on top which, in this case, would be F. All this, you probably already know.
So, when you play a G7 chord and then a C chord, it sounds good, right? It sounds like it resolves. All this sentence is saying is that the reason for this is the resolution of the dissonant sounding tritone in the G7 chord (B and F) to the consonant sounding major third in the C chord (C and E).
If you have any questions about anything, you can always ask me!
~TO
P.S. Great picture
I started to learn a bit guitar/music theory. I don't know what do you think of it all, but it's seems harder then chess theory :) Sometimes I feel i understand it (basicly I understood how to bulid up a minor, a major and a 7th chord), and suddenly I run into this kind of sentences: the dissonant minor fifth interval between the 7th note and the 4th note in a scale will be resolved by going to the tonika (1st note). The 7th and 4th notes of the scale are the 5th and the 7th notes in the dominant 7th chord.
In this moments I sit confused
without a chance to understand and just play guitar for my peasure