What does @: and :: do in bash

Question

So what do they do Im forking this project and i want to translate it to a shell script with no bashisms, unfortunately i don't get what do they really do, they just seem to "clean" the array(which i will have to get rid off) heres the code

for arg do
    if [[ $arg == :: ]]; then
        dmenu_args=( "${@:$i}" )
        break
    fi
   
    case "$arg" in
        -d) mode=disconnect ;;
    esac

    (( i++ ))
done

arg isnt defined anywhere it just pops unannounced, so im guessing it acts as a $@ for the scripts arguments and dmenu_args well, its an array that represents the bars that dmenu is going to print in screen