The width of an A5 piece of paper is 14.8 centimetres, and its length is exactly 21 centimetres. Essentially, if you were to take a sheet of A4 and fold or cut it in two, you'd get the right size for A5.
Whilst not as popular as sizes like A4 and A3 in offices, A5 is a great size for companies to use when advertising and putting leaflets through doors and on noticeboards, etc.
It's also very popular for things like birthday and greetings cards. And because of its smaller and more portable size, Filofax and other diary and calendar companies use it in a lot of their products, as it fits more easily into a bag.
If you're considering getting a Filofax, and wondering which size to go for, here's a video that outlines a few of the differences between their A5 and their Personal size ranges.