With the release of the new version of Gmail, Google introduced sidebars into its interface. Streak includes three sidebar applications: one for Streak Upcoming, one for email tracking, and another for our box sidebar. 

If you're able to see all of these but not close them, it's possible that the side panel is collapsed. You can expand it again by clicking the left-pointing arrow toward the bottom right of your screen:

With the side panel expanded, a thin strip of icons will appear. Clicking an active icon (denoted by both  the shaded circle behind the icon and a blue highlight to the right) will collapse the sidebar entirely.
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In the box sidebar and Streak Upcoming sidebar, clicking the "x" in the upper-right corner will close the sidebar.

The open/closed state of this sidebar will be maintained and preserved between emails. Closing it once (and keeping it closed) will be preserved from email-to-email; opening it once (and keeping it open) will be preserved from email-to-email.