The Las Vegas Strip is the main drag in Las Vegas, where most tourists spend most of their time.
The strip stretches from the Stratosphere in the north down to the Mandalay Bay in the south, a distance of about three miles. There are about 35 casinos along the Strip, some very large and famous, some tiny.
Most of the new casinos are located on the southern end of the Strip, from the Wynn, Trump International Hotel & Tower Las Vegas and Treasure Island on the north down to the Mandalay Bay. This area is the most crowded part of the Strip and is the only part which features attractions for pedestrian traffic (e.g., the Bellagio fountains, the Mirage volcanoes, etc.).
In the center of the Strip, moving North of the Wynn, there are a number of older casinos such as the Stardust and Circus Circus. This stretch of the Strip is largely unchanged since the 1980s, so you can visit there to get a taste of what Vegas was like 20 years ago.
The northern end of the Strip features two perfectly good hotel/casinos, the Sahara and the Stratosphere which are disadvantaged by being on the wrong end of the Strip, away from most of the action.
Factoid: With the exception of the Stratosphere, the Las Vegas Strip is not in the city of Las Vegas. It is in the unincorporated township of Paradise, Nevada.