Yes, there is a rainy season in China. There is also another fun season: typhoon season (台风 - tai feng in Mandarin). While typhoons can happen anytime from May to December, the main season in China is July through September and the peak of the storm season is in August.
Location of Typhoons
Typhoons get started out in the Pacific Ocean or the South China Sea. They gather force and then hit the southern and eastern seaboards of China. The islands of Hong Kong and Taiwan are particularly susceptible to typhoons as are Guangdong and Fujian Provinces on the mainland. Typhoons hit all along China's coast and can send storms inland for several hundred kilometers. Depending on the severity of the storm, this results in high wind and huge amounts of rainfall in a short amount of time.
Travel During Typhoon Season
It's still fine to plan travel during the typhoon season as you never know when or where one will hit. The effects of the storm can last a few hours or a few days. Sometimes there are typhoon warnings and nothing happens at all. Sometimes a typhoon sweeps through and within 24 hours you have beautiful, clear weather after the storm. Sometimes, however, a typhoon hits and a storm stays and hovers for the exact number of days you are visiting a place. So, while you shouldn't worry too much about travel during this season, you do want to be prepared.
What to Do If a Typhoon Hits
If a typhoon does hit your area, you will likely be warned about it by watching CNN weather in your hotel. Hotel staff will probably tell you and if you can get your hands on a local English-language paper, that's another good way to inform yourself about the weather.
Depending on the severity, you can still go out during a typhoon. In the early hours, if it's just steady rain, then you'll be able to walk places (hailing taxis will be difficult) and buses will be running. As the rain continues, the drainage in some places in cities can get backed up so streets, first-floors and sidewalks begin to flood. If you see this starting to happen, you probably want to start heading back to your hotel as the longer this goes on, the harder going (and wetter) it will be on your way home. You should avoid subways as if the storm severity increases, subway tunnels can get flooded and you don't want to be stuck somewhere, worse, inside a station.
Stores, museums and restaurants will be open if the storm isn't severe. If the storm is severe, things will close and managers will send workers home early. In this case, you'll probably want to stay put in your hotel room. (Don't worry, your hotel will stay open.) Make sure you pack an extra book, a couple of movies or whatever else you need to entertain yourself for the possibility of 24 hours in your hotel room without being able to go out.
What to Pack for Typhoon Weather
As with rainy season, you'll want rain-proof clothing and shoes. Actually, if you find yourself out in a typhoon, unless you have a dry-suit on ready for deep-sea diving, you'll probably get wet. What you want are clothes that are quick-drying or you don't mind getting wet (and splashed by street water.)
While you don't want to haul rubber boots along with you, shoes like Crocs are not a bad choice because you can just wipe them down. You can find this kind of shoe everywhere in Chinese markets and street vendors so don't necessarily bring them along but consider buying a pair if you find yourself with the prospect of standing in six inches of water in your new sneakers. Quick-dry shirts and shorts are good to wear in this weather as is a light-weight wind-breaker. If you're carrying a bag, tuck a dry t-shirt to put on if you go inside to a museum or such that will be air-conditioned so you won't get too cold.