The transmission takes power from the engine and automatically selects the appropriate gear based on your car's speed. A good way to conceptualize this is to think of your transmission as the messenger that tells the wheels how fast you want them to turn. The most complex component in your car is your transmission and regular fluid flushes go a long way in preventing much more expensive transmission repair work down the road.
If you notice harsher shifting, check your transmission fluid level first, if it's low, fill it up! If your transmission fluid appears dirty or smells burnt, have the fluid, filter and pan gasket changed. If your transmission fluid is fine, but you still experience poor shifting, you might need a software update or transmission work done.
If you have never had your transmission fluid flushed and your vehicle has over 100,000 miles, flushing the transmission fluid could cause leaks. The old transmission fluid in these situations has likely formed a deposit around the transmission seal and fresh fluid is likely to break down this deposit (and seal) causing it to leak.