You could use the man pages to get details about what the commands combined here do. Here's a little about the purpose of those commands here:

"$([ $? = 0 ] && echo terminal || echo error)"

This would echo terminal or error as per to the execution status - successful or fail respectively of the last command; and the result is as the value to the -i switch of notify-send for displaying the icons.

history|tail -n1

..to get the last command executed.

and sed to parse the text to display it with notify-send message.

To understand these try the following:

true; echo "$([ $? = 0 ] && echo terminal || echo error)"

..this would echo terminal.

false; echo "$([ $? = 0 ] && echo terminal || echo error)"

..this would echo error.

notify-send -i terminal 'Please note the icon..' 'the default icon for the terminal has been used. You can specify any other icon of your choice'

And,

echo $?

..is very useful to know the exit value of the last command executed.

echo "$(echo "the output of this command enclosed within $(...)") is being supplied here in the outer echo command where is used as an argument."

..nested echo as a simple demo for using $() in a command combo.