There are two basic types of mechanic. The first and most common type is the "replacement" mechanic; this variety is characterized by ample capability with a wrench, but with a tendency to simply throw new -- and expensive -- parts at a broken car until they stumble on the part that's actually broken. The second type is the rare "diagnostician," one characterized by the willingness to step back, think logically about the car and how it works, and figure out what exactly what's wrong with it before cash hits the parts counter.
The ignition coil's job is to amplify voltage supplied by the battery, trading off amperage in the process but creating the momentary, white-hot flash of electricity that engines need to fire. Up until fairly recently, most cars used a single ignition coil, relying on either a mechanical distributor or a computerized "relay" module to trigger electrical flow through the coil and send it to the appropriate cylinder. More modern "coil pack" engines use two or more coils mounted on a common base; the computerized "module" that controls spark distribution is typically incorporated into this base. The most modern "coil-on-plug" ignitions place one coil right on top of each spark plug, increasing voltage to the plug and giving the system some margin for error.
When an ignition coil fails, it'll cause a misfire, or failure to ignite the air-fuel mixture. This failure to ignite "kills" the cylinder; the "dead" cylinder causes an interruption in power production in the engine, causing it to shake and jerk. Ignition coil misfires tend to be the most pronounced on engines with a single coil and low cylinder count. The more coils and cylinders an engine has, the less you'll notice a bad coil. When a coil first begins to fail, it'll usually be at higher rpm, after the engine has warmed up; when it's completely dead, the misfire -- and attendant engine vibration and jerking -- will be most noticeable at low rpm, when the engine is under load.
Jerking Going into Drive
Absent of any other symptoms, a car that jerks going into drive usually has one of two problems. The first and most common is a high idle. An engine that idles at a high rpm will send a bit too much power through the transmission when you engage drive, causing the car to jerk forward. Bad CV joints are probably the second most likely culprit behind a car that jerks going into drive. Bad CV axle joints can develop large clearances between components that are supposed to mesh tightly together; so, when you put the car into gear, the transmission-output side will hammer one internal part of the CV joint against the other. This hammer-blow can manifest as a jerk when shifting.
It's possible that a bad coil in itself could cause the car to jerk when shifting into gear, but any misfire bad enough to cause this kind of jerking will probably manifest as a noticeable engine shaking under other conditions as well. However, there's no telling exactly how your car's control computer or module will react to a dead coil. It depends on the type of ignition system and the severity and regularity of failure. Some computers might react by increasing idle speed to keep the engine running in the presence of a dead cylinder, in which case you might get a sharp jerk going into gear, accompanied by by a near-stall when it does engage. But again, odds are good that any misfire severe enough to trigger this reaction will be noticeable under other conditions as well, and you'll almost certainly get a check-engine light.
Other Possible Causes
Anything that "tricks" the engine into idling higher than it should can manifest as jerking going into drive. Bad throttle-position, mass airflow, crankshaft or camshaft position and manifold air pressure sensors can trigger a high-idle response from the computer. On fuel-injected engines, vacuum leaks can do the same. That little bit of extra air going into the engine will lean out the air-fuel mixture. The oxygen sensor may tell the computer to increase the amount of fuel injected, increasing the engine's power at idle and potentially causing a jerk when you go into gear. A bad ignition module can manifest in many ways, including idle issues. You might look into the transmission itself if the car jerks going into gear, and you don't get a check-engine light or vibration indicating misfire. Old transmission fluid or a clogged filter can cause jerking absent of any symptom of engine malfunction.