Understanding Finite Automata Notation

Question

I am having having troubles understanding the following finite automata example:

I don't quiet understand what they mean by $B_i$ is in $q_j$. $B_i$ is a finite automation and $q_j$ is a state. I neither understand what the functions mean.

Answer 1

"$B_i$ is in $q_j$" means "$q_j$ is the current state of $B_i$"

$\delta_i(q_j,0)=q_k$ means "if the current state of $B_i$ is $q_j$ and the current input is $0$, the next state is $q_k$"

... and so on.