A resolution chart is a picture that has periodic objects in it that can be used to check the quality of optics. An old and famous resolution chart is the USAF 1951 test target pictured below.
This resolution test chart was developed by the US Air Force to test lenses used to take pictures from airplanes. The National Bureau of Standards (now known as NIST) had their own resolution chart, and ISO has a chart designated 12233 for testing of electronic still cameras. A picture and description of the ISO chart is available here.
There are several ways to use these charts. One way is to simply take a picture of them through the lens you’re trying to test. This works for lenses designed to image at finite conjugates (the distance from the lens to what it is aimed at is less than infinity). For infinite conjugate lenses, put the chart a the focus of a collimator and take a picture through the collimator. Or, for lenses designed for visual use, the lens is placed so that the target is at its rear focal plane and the inspector looks at the image (at infinity) formed by the lens.
The advantages of resolution chart testing are that it is inexpensive and insensitive to vibrations. Disadvantages include the challenge of deciding whether a certain target is resolved or not, a decision which must be made by looking at the image through a camera and assessing by eye. To read about more methods for resolution testing, go here.