What about something as simple as the expected value proposition or 'why should we give a sh!t about your idea?' When I've pitched to angels, these seem to be a common theme.
yes, absolutely important. something we really struggled with early - both the one sentence and the 30 second that people instantly GET. this is not just for investors, but for anyone - potential partners, hires, your mom, etc. and keep in mind this is def a work in progress - you'll improve on it and often change it substantially over time!