Don't have time to read that page, but I don't think it has anything about cascading on it, so I'll try my best to explain it.
If you input into a shift register 10101010, the register will be full (assuming it's an 8 bit register). Now, you can kind of picture the shift register as a thin building with 8 rooms, each of them a "bit". As you put in the first 1, that goes into the first room. Now, when you enter that 0, it forces the 1 out of the room, and into the next. Repeat for all 8 bits, and the building is full.
The problem you've got now is, if you put in another 1 or 0, because there's no room, the number in the last "room" is forced out, and lost forever.
The way around this is cascading. The 74HC595 for example, has a Q7' pin, which outputs bits that are shifted outside. You can hook up the cascading pin to the data pin of the second shift register, and form a sort of passageway between the two buildings, allowing the bit that is moved outside to enter the new building. Shift in 16 bits, and you've got 2 full registers.
You can continue to add new shift registers in this manner a theoretically infinite amount of times.
I tried my best to make that understandable, hope it helps! :D