A crop view of the solar prominences seen during totality on 8/21/17. In this image, taken with a Canon 40D, 100-400 zoom lens at f/8, 1/4000 sec, ISO 100, the inner corona is all but invisible. See here for comparison.
The solar prominences are part of the sun’s chromosphere layer. The chromosphere is, of course, always present — some of the chromospheric activity that extends high enough above the surface may become visible at the “edge” as the sun rotates — this is never seen during a normal day because the photosphere drowns it out (unless one views through a special “hydrogen alpha” filter), but can become visible through binoculars during eclipse totality. Whether or not solar prominences are visible during an eclipse is pure luck.
The solar prominences are red because the chromosphere emits light at the “hydrogen alpha” wavelength, 656.28 nm, which is in the red part of the spectrum. “Hydrogen alpha” photons are emitted when a specific electron transition occurs in the hydrogen atom (between the 3rd and 2nd energy levels).