What are the different Gauges and Scales? What do they mean?

O Scale - 1:48
Gauge: 1.25" (31.8mm)
          Marklin, the German toy manufacturer who originated O scale around 1900 chose the 1/48th proportion because it was the scale they used for making doll houses. In O scale 1/4 inch equals 1 foot. Interestingly, O scale was originally called Zero Scale, because it was a step down in size from 1 scale. From the 1920s until after World War II, O scale dominated the model train market. But as model trains became more affordable for the average person, the space required to set up the tracks became a major consideration in purchasing model railroad trains.

HO Scale 1:87.1
Gauge: 0.649" (16.5mm)
          HO has the broadest range of products from the greatest number of manufacturers. In HO scale 3.5mm equals 1 foot. The designation HO stands for "Half O". Of course if it was actually one-half of O scale it would be 1/96th, but because HO is actually a metric based scale and O is based on English units of measure the fractions become awkward. The model railroading industry says HO is "approximately half O".

N Scale - 1:160
Gauge: 0.353" (8.97mm)
          The "N" is short for nine millimeter (although the actual gauge is 8.97mm). In N scale 2mm is approximately 1 foot. N scale is the second most popular scale worldwide. Many modelers select N scale as an alternative to HO scale because it allows more complex layouts to be built in the space available to them. Traditional thinking is that N scale trades detail for space. However, modern manufacturing and painting processes are producing N scale models with surprising levels of detail today.

Z Scale - 1:220
Gauge: 0.257" (6.52mm)
          Prior to 2008, Z scale was the smallest commercially available scale in model railroading. Z scale is popular with apartment dwellers and others with very limited layout space. Z scale is awkward mathematically, approximately 0.0545 inches to the foot, but that doesn't hurt its popularity. Z scale is the fastest growing scale in model railroading today. Some Z scale manufacturers offer briefcase layouts; entire track layouts with landscape, buildings, and a power supply all in a briefcase. These are high-end executive toys that sell for around $1,000.