(Click the pic for full-size. You know you want to.) Most cinder cones eruptions follow roughly the same story line: they start with a volatile-rich phase, tossing out bubbly, vesicular lava, with gasses acting as the propellant. A large heap of these cinders form around the vent. Since the slope is limited by the angle of repose- the steepest that a loose material of a given nature can be piled without collapsing- cinder cones tend to all look quite similar. The material they're made of is all vesicular mafic lava (basalt to andesite), so they vary in size, but not much in overall geometry.
Later in the eruptive cycle, though, as the supply of gasses starts to sputter out, the basalt is no longer thrown from the vent by their escape. This is where some variation in the morphology of cones can arise. The basalt is still being driven to escape by pressure from deeper down, so it starts to push up the throat of the newborn cone. However, the hydrostatic pressure of that column of basalt is often enough to overcome the confining pressure of the pile of loose cinders. The newly vented basalt is denser than the now cool cinders, which often have a greater amount of void space than actual rock- this is called scoriaceous basalt, or scoria. So rather than rising to the vent of the cone, the younger lava simply plows through its bottom and side, and erupts as flows. I refer to these as breach flows, though I'm not sure that's the correct term. I do recall that when an entire side of the cinder cone is blown out and carried away by the later flows, that's called a breached cone. It only took a few moments looking around in FlashEarth to find a nearby example- tree covered, so clearly older. (just above the cross hairs, and there's another, north-facing, breached cone over to the lower right)
In the case of Lava Butte though, not enough of the cinders were excavated by the later flows to damage its symmetry. So we're standing in the middle of the area where those gouts of lava emerged from the cone's flanks. The edges of the flow cooled more quickly, and the middle more slowly. So the edges of the flow are topographic highs, while the center remained hotter and able to flow away, resulting in a low area. This is referred to as a lava gutter. And with deference to Oscar Wilde, I get a little starry-eyed every time I take this short walk. I know of no other spot that more clearly imbues the viewer with such a visceral sense of what the past looked like.
Panorama stiched with HugIn, and run through Paint.Net's autolevel routine. August 21, 2011. FlashEarth location.