Short explanation...
Listeners fill out diaries documenting what they listened to and for how long. Sometimes in crayon.
Arbitron totals these samples and computes various percentages. The number you see published to non-subscribers is the "12+ AQH", which is an average of what percentage of people listening to the radio during a given 15-minute period (Average Quarter Hour), ages 12 and over, are tuned to the various stations.
The service to which stations subscribe goes much deeper than that. The numbers are broken out by age groups and gender. Most of the stations care about the 25-54 and 35-64 demos because that's the age group advertisers want to reach.
The 12+ numbers rarely tell the story of success or failure because at all but the top 2 or 3 stations in a given market, the target is a narrower band of listeners (WSHH, for instance, is aimed at women 35-64. B94 and Kiss care about 18-34 females. The Zone wanted men 25-54).
There are also measurements of Time Spent Listening (TSL) and Cume (the total number of persons tuning in, with no time parameter). The two numbers combine to compute the AQH share.
The are also gross rating points, which measure what share of the local population is tuned in, not just the percentage of people listening to the radio. This matters, for instance, in setting ad rates for drive time vs. non-peak dayparts (you can be #1 at night and have fewer actual listeners than the #10 morning show, when most people are tuned in).
So that's a real scratch-the-surface overview.
