This helps you remember the meaning of the patterns (or me, at least). For example, consider ⠗. The bottom row tells us that this character is in the second decade, and the top two rows tell us it’s the eighth character in the decade. The eighteenth letter of the alphabet is R, so this pattern is R.
For more, see Wikipedia.
Louis Braille was an avid musician, and an accomplished cellist and organist, so he wanted a system that could be used to write music. There have been several systems for writing music with Braille, with some minor differences, but today the Braille music code is mostly standardised. You can use it to express almost anything you can write with standard musical notation.
Unlike printed music, a Braille musician usually has to read and memorise the score – if they read the score with Braille while playing, they’d only have one hand left for the instrument!
There are many writing systems using the six-dot Braille cell that allow you to write mathematical and scientific notation. Because there are lots of mathematical characters, it requires a lot more context – a single symbol might need lots of Braille patterns to represent. Sort of like the number sign I mentioned above, but longer.
Compared to a printed alphabet, braille takes up much more space on the page – a single pattern is bigger than a single character, there are extra formatting and punctuation marks, and the spacing is a lot looser.
You think your copy of Harry Potter and the Order of the Phoenix is big? It’s nothing compared to the braille editions, “each of which amounts to a 13-volume stack of paper more than a foot high”.
If you want to read something using braille but you don’t want (or can’t) print it on embossed paper, you can use a braille display. This is an electro-mechanical device that displays braille patterns. It can create a sequence of patterns by raising round-tipped pins for the text you want to read.
You select a line of text to read, and it creates the correct dot patterns. You read the line with your fingers, and when you’re done, you refresh the display and it shows the next line of text.
When I originally wrote this post, I capitalised the name of the system as “Braille”. As I was doing the reading, I learnt that lowercase “braille” is much more common, with a capital letter only if you’re talking about Louis Braille. I think I’ve fixed all the text above, but please let me know if I’ve missed one – or if you think I’ve made any other mistake.