What do the various lines mean? What are the axes?
The source we all quote on how to read an MTF chart is Michael Reichmann's article at Luminous Landscape. Most of the following information is cribbed from that article.
However, keep in mind that these particular conventions only apply to Canon MTF charts. Other lens makers may have different ways to denote these things, and may or may not show all the same information. And, as Reichmann says in that article:
... be aware that an MTF chart doesn’t tell us everything that there is to know about a lens. Important variables such as vignetting, linear distortions of various sorts, and resistance to flare are among the things not measured.
On a Modulation Transfer Function, the horizontal axis denotes the distance from the center of the lens, so the zero point on the left is the performance of the lens at center, and the far distance on the right denotes corner performance. Note also, this way you can see the difference in corner performance between use on a crop and on a full frame sensor.
The vertical axis denotes the amount of contrast, on a scale from 0 to 1 (I.e., you can think of it as the scale of 0% to 100). So, air, for example, would give you a straight horizontal line at 1. The flatter and nearer the top of the chart the line is, the better the overall performance.
The black lines indicate performance wide open.
The blue lines indicate performance stopped down to f/8 (I think Nikon doesn't bother to show this on their MTFs).
The thick lines are measurements taken at 10 lines per millimeter (low resolution). The higher up the chart these are, the better the contrast of the lens.
The thin ones at 30 lines per millimeter (high resolution). The higher up the chart these are, the better the perceived sharpness of the lens.
Solid lines are meridonial (i.e., the test chart lines are slanted 45° from upper left to lower right). And the dashed lines are sagittal (the lines are slanted from upper right to lower left). They evaluate astigmatism and field curvature, and the closer these two lines are to each other, the smoother the bokeh will tend to be.