What is this strange symbol called :=? I want to Google it but I don't even know what to call it.
It looks like some sort of assignment used in computer science or math.
Here it is again
:=

It is used to describe CS algorithms here:
http://www.cs.nyu.edu/~cconway/teaching/cs1007/notes/arrays.pdf

It is use to define/initialize some variable or function in the programming language. $"="$ is often use to compare stuff to check for instances "if"s like if(x=2) then... while "$:=$" is often used to initialize a parameter, see for example page 19 of your notes, the bubble sort:
The author sets $i$ and $ swap$ to $0$ and then checks some condition with the "if". If he had wanted to check eqality at step $2$, he would ahve used " if $X_i=X_{i+1}$. Then he, if that condition is met, he sets $swap$ to be $1$ by doing $swap:=1$.
