What does the On Axis, 30% Field, 60% Field, etc... mean?

'On Axis' means the exact center of the field of view where the optical center axis of the lens intersects the test chart.

'30% Field' means a measurement was made at 30% of the distance from the center of the field of view to the corners of the FoV. For a full frame camera the distance from center to extreme corner on the sensor is 21.633mm, so 30% field on the surface of the camera's sensor would be somewhere on a circle with a center at the center of the lens' optical axis and having a radius of 6.49mm. That is, 30% Field is measured at a point on the test chart that would fall on a point 6.49mm from the center of the sensor.

'60% Field' is similar. It means the distance from the center to the point tested is 60% of the distance from center to extreme corner. For a full frame camera this would be 12.98mm from the center of the imaging sensor.

What are the (S) and (T)?

(S) is Sagittal. That means lines drawn from the center of the field of view towards the edges. Sagittal lines look like spokes on a wheel.
(T) is Tangential. Tangential lines are lines that are perpendicular to the Sagittal lines.

Lenses often have differing acutance rendering (S) and (T) lines. The difference between the (S) and (T) is often described as a lens' degree of astigmatism.

The numbers on the third column describe resolution as percentage contrast between alternating lines of white and black lines. Perfect resolution would result in 100% contrast. A result of 0% would indicate that line pairs are imaged on the sensor as an even gray color with no distinction between the black lines and the white lines.

The numbers in the fourth column describe the pitch of the line pairs of white and black lines as they would be measured on the surface of the imaging sensor or film.

In your example, we can see that when imaging line pairs at 112 LP/mm, the lens in question has 77% contrast at the center of the field. That means that the difference between the black lines and the white lines is 77% of the difference between pure white and pure black.

At 60% field we see that with 223 LP/mm the lens is capable of 48.8% contrast on line pairs oriented in a Sagittal direction and 43.0% contrast on Tangential line pairs. This means the "spokes" of a wagon wheel imaged with the lens would have slightly more contrast than the "rim" of the wheel if the hub was placed at the center of the field of view, as shown (at a much more severe degree of astigmatism) in the center figure below.