Despite what you may see on the news, not all of Mexico is a desert full of drug gangs and dustweed. While there are certainly very dangerous areas of the country, particularly in border zones, Puebla is generally safe. Yes, there have been incidents of serious crime, like kidnapping or highway robbery, but all and all it is a fine place to be.
Petty crime, such as pickpocketing and street robbery, is quite common, so do be careful. Always, always keep a close eye on your bag whenever you are on a jam-packed rush hour bus or the crowded downtown streets. Pickpockets are speedy and efficient and take advantage of those situations. Also take care not to pull out fancy technology (like an iPad) on buses or on the street, as this can be an invitation to robbery. As in any city, avoid lonely streets or dark places, and heed your common sense.
The US Travel Editor for Lonely Planet even wrote an article about certain areas of Mexico being safer than some US cities: