A torque converter is the fluid coupling between an engine and transmission that allows the engine to idle at low speed without engaging the transmission. A torque converter uses an engine-driven turbine (fan) to push fluid through a matching turbine attached to the transmission. At low speeds, the engine turbine's fluid simply passes through the transmission's turbine without moving it, constantly recycling back through the drive turbine. Though this design does have a number of advantages over anything comparable, it is not completely free of inherent flaws.
Torque converter shudder fells like a slight to heavy vibration in the transmission, and is usually accompanied by an interruption in power transfer. It generally occurs at part throttle and light acceleration, between 15 and 50 miles per hour, just before the shift to one of the top gears where the converter reaches "lock-up." Since it is temperature-related, it tends to happen on hot days, after idling in traffic for long periods of time.
As mentioned, converter shudder is usually temperature related. As transmission fluid recycles back through the engine turbine, it picks up frictional heat. Once the amount of heat generated by this friction surpasses the transmissions cooler's ability to shed it, the fluid thins and power transfer becomes inconsistent. Other sources of heat build-up are failing transmission clutches or bands, and blocked coolant lines or radiator. Overloading the transmission also produces excess heat, as anyone who has towed a heavy trailer uphill can attest.
Transmissions can shudder in a very similar manner to torque converters. To determine whether the shudder is tranny or TC related, run your vehicle for a little while till it begin to shudder and immediately park it. With your foot on the brake, put the transmission in Drive, and apply light throttle. If you feel shuddering, then it's the Torque converter; if not, then the problem is within the transmission.
Solving the Problem
Unless there is physical damage to the converter or transmission, shudder is a fairly easy problem to solve. Once the transmission fluid has been overheated enough times, it becomes permanently depolymerised and need to be replaced. You can do this yourself by draining the transmission and flushing it, or taking it to any competent mechanic for maintenance.
The Band-Aid Fix
All auto-parts retailers sell some sort of transmission additive designed to thicken the fluid. Lucas brand is the most popular and is recommended by specialists like Mr. Transmission, but is usually the most expensive. Those with older (pre-2000) GM and Chrysler transmissions can try adding a quart of Ford Type F transmission fluid, since it contains friction modifiers that the stock Dextron does not.