Hi Mark!

The white structures that dominate the solar images during an eclipse are called helmet streamers. Streamers appear so bright because their density is much larger than the surrounding density. Coronal streamers consist of magnetic loops and by comparing the images during the eclipses taken at different times you can see how the solar magnetic field changes at different phases of the solar activity cycle.

The first image below shows the solar corona during solar activity maximum in 1980 and the second image the corona during solar minimum in 1988. You can see that the structure of the corona is much more simple during the minimum activity.

With an instrument called coronagraph one can observe solar corona even when there is no solar eclipse. Coronagraph creates an artificial solar eclipse by blocking away the bright solar disk with an occulting disc. Currently SOHO and STEREO spacecraft carry coronagraphs.