Centuries ago measuring the size of objects in the sky was fairly nonstandard among various cultures. When describing comets in ancient times the Europeans used such terms as "the size of a man", while the Chinese included phrases such as "as large as a pear," "the size of a peck measure," "the size of a peach," or "the size of a vessel with a capacity of three pints." Whew! These are probably all pretty exciting for someone inside those particular cultures, with with no frames of reference for these measures, other people have no idea what they were talking about. Even the European measure is difficult since we have no idea how far the man should be from the observer to be useful as a measuring stick for the sky.
For the last few hundred years, astronomers have used the terms degrees, minutes, and seconds to measure the sizes of comets.
What is a degree?
This measure is based on the fact that a circle is composed of 360 degrees. From the perspective of an observer on Earth the sky above us is a sphere with a circumference of 360 degrees. At any one time 180 degrees of sky are visible above your horizon. Such high numbers are usually only used to measure the tails of bright, naked-eye comets.
The moon and the sun make nice measuring sticks as each is very close to one-half degree in diameter. Among deep-sky objects, the Andromeda Galaxy is about 2.5 degrees long.
What is an arcmin?
This measure technically represents 1/60 of a degree. For comets it is typically used to measure the diameter of the coma and the length of comet tails.
When at its brightest, Jupiter usually displays a diameter near 0.8 arcmin. Among popular deep sky objects, the Ring Nebula (M57) has a diameter of just over 1 arcmin and the Dumb-bell nebula in Vulpecula is about 8 arcmin long and 5 arcmin wide.
What is an arcsec?
Technically it is 1/3600 of a degree and 1/60 of an arcmin. It is typically used to measure the diameter of the nuclear condensation within a comet, as well as the coma and tail of very distant comets.
Planets represent other astronomical objects whose diameters are given in arcsec. As noted under arcmin, Jupiter usually attains a diameter of 45 to 50 arcsec when closest to Earth. On the smaller side, Uranus typically reaches a diameter of 3 arcsec each year, while Neptune is normally around 2 arcsec.