Two-color overprint ink trapping targets
Ink "trap" is an objective indication of the ability, or inability, of a printed ink to accept the next ink printed compared with how well the substrate accepted that ink. Poor ink trapping results in presswork color shifts in reds (magenta plus yellow), greens (cyan plus yellow), and blues (cyan plus magenta) as well as a loss in total color gamut.
The two-color overprint solids allows for the objective measurement and evaluation of ink trap efficiency as well as the overprint hue error and greyness.
Typical trap values for three print conditions running a CMY ink sequence with Black first or last down:
Offset sheetfed: R=70, G=80, B=75
Heatset web offset (publications): R=70, G=87, B=72
Coldset web offset (newspaper): R=50, G=89, B=50
Slur and doubling targets
Slurring and doubling are print defects that occur when halftone dots and type blur as a result of a slight second contact or movement between press cylinders or the paper and blanket. (More about slur HERE and doubling HERE)
There are many different styles of slur and doubling detection targets. Here are two of the most popular:

Of course, every halftone dot or letter character on the printed sheet will reveal slur and doubling, however the targets in the color bar signal the defect easier and quicker.
Grey balance targets
Grey balance targets are made up of a patch of three screened process colors that are balanced so as to appear as neutral grey under standard printing conditions. They are typically printed adjacent to a black screen tint of a similar value to allow for a quick visual, or measured, evaluation of how grey balance has shifted.
Grey balance targets can be useful since variation in any of the three process colors because of dot gain, slur, doubling, density, trapping, and registration will be reflected by a shift in hue away from neutrality. The 3/C patch will take on a bluish, reddish, or greenish color cast.
The idea behind this target is that any grey balance color shift away from neutrality suggests a possible color shift in the live image area. However, in production printing the grey balance target may not be a reliable indicator of presswork issues. More detail on this topic can be found HERE and HERE.Other targets
Other targets that may be included in the color bar are:
Dot gain
These targets are intended to capture dot gain variation information. The dot gain targets may consist of just two patches for each process color to measure the dot gain a one location on the tone scale, or, with the addition of more patches, to measure the dot gain at the quarter, mid, and three-quarter tone values. Dot gain can be useful because issues like slur, doubling, or incorrect solid ink density, will be reflected by a variation in the measured dot gain.Brown balance targets
Brown balance patches are similar to grey balance patches in function except that they are made up equal percentages of cyan, magenta, and yellow. Unlike grey balance patches which allow the press operator to make a subjective visual assessment of hue shift, brown balance patches can only be evaluated objectively with instruments.Proprietary
Proprietary targets such as that used by System Brunner are typically used to drive on-press closed loop color control systems.Spot color
If a spot or brand color is being used then it will warrant at least a solid patch in the color bar so that its solid ink density can be measured. Space permitting, the solid patch will be adjacent to a screened back patch so that dot gain information can be measured.