I can't check your links (for some reason they didn't make it through to your published post...), but I think I can help.
Think about how a time signature works (or, learn -- try musictheory.net for some good tutorials). For example, a 4/4 time signature means that there are 4 beats in a measure, and the quarter note gets one beat.
So, you can imagine a measure with only complete beats -- just 4 quarter notes. But if you want something more interesting, you'll probably break some of those beats into eighth notes -- these pieces of beats would be sub-beats. In 4/4, this works like you'd expect. Each quarter note can be broken up into 2 eighth notes. This is called "simple meter" (the way the beat divides). 2/2 is another simple meter -- each measure has 2 beats, each beat is a half note, and (this is the "simple" part) when you subdivide that beat, it just splits evenly -- so each half-note breaks into 2 quarter notes.
This seems kind of obvious -- isn't that how all beats would subdivide? -- until you see a "compound" meter, like 6/8. In 6/8, one measure gets 2 beats, but each beat is a dotted quarter note. When you subdivide that, it breaks into three parts (3 eighth notes) instead of two.
I think there's a tutorial on musictheory.net that covers how to figure out compound meter -- I hope this helped!
-Rob