The numbers are a way of "naming" tricks so that you can know how to do them just by their name. It is a system called "siteswap" or site swap... Whichever works best.
Each juggling pattern has a specific height at which you should juggle it. 3 balls would peak around your nose/forehead. 4 balls would peak at the top of your head or a bit higher. 5 balls are anywhere from 1 foot to 2 feet above your head... etc. etc.
Now the numbers correspond to each ball and each throw. For example, when juggling 3 balls, the name usually given to it is "the cascade". But if you were to hear "Hey! Do the cascade!" you may not know what that means. If we call it by its siteswap name, 333, then we know the first ball is thrown at a 3 ball height, the second ball is thrown at a 3 ball height, and the third ball is thrown at yet another 3 ball height.
You still with me?
Moving along, another 3 ball trick (siteswap) is something called a 531. The first ball is thrown HIGH at a five ball height. The second ball is thrown lower at a THREE ball height. the third ball is a 1. This means you QUICKLY pass the ball (or a fast and straight toss) from hand to hand.
Odd numbers will always cross over to the other hand. Even numbers will always come back down to the same hand. (Such as when doing four balls (Really just two balls in on hand... but with both hands...) the siteswap pattern is 4444 and the balls will always stay in the hands they start in.)
So when doing the five ball patterns in the video, you see 744 as one of the first numbers. This means while I am doing the five ball pattern. (55555) I will break and throw a 7 height (with my right hand) then a 4 height (with my left hand) then another 4 height (right hand) and then continue back into the five ball pattern (5 with my left hand, then 5 height with my right hand... etc. etc.)
Now here is something cool about juggling. You can make up your own tricks if you know basic math!
If you want to know if a trick will work, you add up all the numbers in the pattern (5+5+5+5+5 = 25) and divide by the number of balls you are using (5 in this case) if it works out to be divisible by that number, the trick will work! (25/5=5!) Or more complex 7+4+4+5+5=25...25/5=5
With three balls we would see 3+3+3=9... 9/3=3 OR 5+3+1 = 9... 9/3=3
But when you juggle, you want to make sure to do something called "running" a trick. This means that you want to make sure to do it a number of times on each side. Going back to the video, you will see me do 744 (i think) 4 times in a row. So the siteswap would be 744744744744. But because we are all smart cookies, we can shorten it to just 744 and know to connect it. So while the 7 will start with the right hand, the next seven would come from the left hand and so on, until you decide to go back into the five ball pattern (Or start another siteswap!
All in all, it is an easy way to convey what tricks you will do, in what order, and know the degree of difficulty. (Some heights are harder than others.)
Then there are things called multiplexes where you throw two or more balls out of the hand at the same time... but that is more complex and difficult to describe in words.
A quick handy guide to what siteswap numbers mean
0 = no ball in the hand
1 = pass the ball quickly to other hand
2 = hold the ball (or a REALLY small toss)
3 = 3 ball cascade height (basic pattern)
4 = 4 ball height (2 in one hand)
5 = 5 ball height (higher and faster 3 ball pattern)
6 = 6 ball height (just like four balls, but three in each hand)
and so on and so on
After a while they start going into letters... that just means extremely high throws!
a = high crossing throw
b = high same hand throw