For those who prefer diagrams, below is an excerpt from Is there a purpose for the E61 middle brew lever position? that covers many of the same points:
HB wrote:For the benefit of those who are wondering what these valves look like, a few diagrams from Lino. Please do not copy these images.
The first image shows the E61 lever at the rest position. The two lower valves are open to allow the brew chamber and expansion chamber to drain. The uppermost valve is closed. Water from the HX circulates through the upper port on the left, passes alongside the "mushroom" to heat the grouphead; as the water cools it descends through the lower port on the left. The temperature difference creates a thermosyphon that circulates water between the boiler and grouphead.
The next image shows the E61 lever at the mid position. The two lower valves are closed and the upper valve is barely open. If this pump has line pressure, water will flow through the upper port, grouphead cap and screen, gicleur (yellow), descend towards the brew chamber (orange cam), and finally through the L-shaped channel to the brewhead. It's easy to see the purpose of the Allen screw (gray); it caps the hole drilled during manufacturing for the first leg of the channel.
The final image shows the E61 lever in the brew position. The upper valve is held open by the orange cam. The valve at the bottom of the expansion chamber is held tightly closed by a spring. The spring above it holding the second valve closed is weaker; it will open at about 4 bars of pressure. It only takes a second or two for the brew chamber containing the orange cam to pressurize. As the pressure builds, water eeks pass the valve below the orange cam, allowing the pressure to drop. This action is the novelty claim of the E61 patent since the pressure is automatically lower as the expansion chamber fills. Once the lower chamber fills, the pressure equalizes in all chambers and the valve below the cam closes.
The familiar "whoosh" that follows the lever being lowered is water evacuating the brew chamber and expansion chamber. Again at rest, the expansion chamber and brew chamber are empty. Water continues to circulate along the jacket of the uppermost chamber as the thermosyphon re-establishes itself.
I respectfully offer another explanation to Bill's answer to the purpose of the second exhaust valve (5:59). It's key to the E61 patent as explained in the paragraph above starting with "The final image shows the E61 lever in the brew position."
On a related note, Randy's article Simple Lubrication of the E-61 Group provides instructions and accompanying video for fixing squeaky E61 lever arms:
If your E61 goes drip drip drip, Randy's follow-up article Overhauling and Lubricating the E-61 Group and EspressoCare's Rebuild Kit are all you need. See Constant dripping from E61 grouphead for discussion and more photos.