You can open the speaker view through a link on the present view or by manually appending "speaker" to the end of your deck URL (slides.com/<username>/<deckname>/speaker).
The previews of current and upcoming slides inside of this view are automatically kept in sync as your presentation is navigated. This syncing also works across devices so that you can, for example, have the speaker view open on a different computer from the one that you're using to show the presentation to your audience.
If you're using the speaker view in conjunction with a live presentation you'll see a status indicator in the bottom right hand corner telling you how many subscribers there are.
The speaker view also doubles as a remote control when accessed from a mobile phone.
If you make heavy use of speaker notes, you may want to change the layout of the speaker view to one which gives more prominence to notes.
If you export your presentation to present offline you will need to use the offline speaker view. This can opened by pressing the S key on your keyboard when the offline presentation has been opened in your web browser.