Lines on the map outline various rock units, or formations. Geologists prefer to say that the lines show the contacts between different rock units. Contacts are shown by a fine line unless the contact is determined to be a fault, a discontinuity so sharp that it's clear something has moved there. (see more about the three types of faults)
The short lines with numbers next to them are strike-and-dip symbols. These give us the third dimension of the rock layers—the direction they extend into the ground. Geologists measure the orientation of rocks wherever they can find a suitable outcrop, using a compass and transit. In sedimentary rocks they look for the bedding planes, the layers of sediment. In other rocks the signs of bedding may be wiped out, so the direction of foliation, or layers of minerals, is measured instead.
In either case the orientation is recorded as a strike and a dip. The strike of the rock's bedding or foliation is the direction of a level line across its surface—the direction you would walk without going uphill or downhill. Dip is how steeply the bed or foliation slopes downhill. If you picture a street running straight down a hillside, the painted center line on the road is the dip direction and a painted crosswalk is the strike. Those two numbers are all you need to characterize the rock's orientation. On the map, each symbol usually represents the average of many measurements.
These symbols may also show the direction of lineation with an extra arrow. Lineation might be a set of folds, or a slickenside, or stretched-out mineral grains or similar feature. If you imagine a random sheet of newspaper lying on that street, lineation is the printing on it, and the arrow shows the direction it reads. The number represents the plunge, or the dip angle in that direction.
The full documentation of geologic map symbols is specified by the Federal Geographic Data Committee.