A comet’s ion/plasma/gas tail points directly away from the Sun. A comet’s dust tail deviates somewhat (and sometimes a lot) from this, falling behind the comet along its orbital path around the Sun.
For the best view of either tail, our line of sight should be perpendicular to the length of the tail. However, that seldom happens, and we are viewing the tails with some degree of foreshortening. The orientation of the gas tail is called the phase angle, and it is the Sun – comet – observer angle.
A phase angle of 0° indicates we are looking straight down the tail of the comet (maximum foreshortening) with the head being oriented closest to the observer.
A phase angle of 90° indicates that our line-of-sight to the comet is perpendicular to the Sun-comet line, so we are viewing the comet’s gas tail with no foreshortening.
A phase angle of 180° indicates that we are again looking straight down the gas tail of the comet (again, maximum foreshortening) only this time the tail is closer to the observer and the head further away. Of course, the only time this orientation could happen is when the comet is transiting the Sun, thus rendering it essentially unobservable.
Phase angles of 0 to 90° mean that the comet head is closer to the observer than the tail; angles of 90 – 180° mean that the comet’s tail is closer to the observer than the head.
Here’s a table showing the phase angle, and some other information, for currently-observable comets brighter than 15th magnitude as seen from Earth. The column labeled Elongation indicates the Sun – observer – comet angle. In other words, the angular separation between the Sun and the comet.
A comet that is farther from the Sun than the observer can never have a phase angle as great as 90°, but a comet that is closer to the Sun than the observer can. Looking at the diagram above and considering a comet in a circular orbit around the Sun (highly unlikely, I know, but bear with me) and closer to the Sun than the observer, the phase angle would be 90° when the comet is at greatest elongation.
Incidentally, comet designations that have a number followed by the letter “P” (such as 29P, 68P, and 260P) are periodic comets (more precisely described as short-period comets), defined to be comets with orbital periods of less than 200 years or that have been observed at more than one perihelion passage.