Even though toilets often operate with the principle of water falling from a higher point to remove water and waste at a lower point, there are components inside the tank that can make noise while the toilet flushes. Also, the flush itself on certain types creates a suction-like noise, which is typical. Other noises, however, are not normal.
In a gravity toilet, as the volume of water swirls into the bowl, it displaces air within the toilet's drain passage with water, which creates a siphon action needed for a full flush that removes all the bowl contents. The noises of this water swirling and crashing inside the bowl and drain are often easily heard and represent the normal full flushing performance of the fixture.
With the toilet flushed, the tank water supply replenishes once it reaches a specific low level. This water often makes a noise as it sprays from the tank's fill valve into the tank. You might also hear the fainter sound of water filling the bowl, which is normal also and represents a small flow of water that is diverted from the tank into the bowl, travelling through the overflow tube. If the sound of the water filling the tank is too loud, you can turn the shutoff valve slightly clockwise to lower the water pressure and lessen the noise.
If the flushing bowl water gurgles, it indicates a partial clog. The clog can either be inside the toilet itself or inside the drainpipe. You can often reach a clog deep within the toilet with a toilet auger, or snake. If the partial clog is in the line directly under the toilet, you can lift and remove the toilet and then snake the drainpipe underneath. If the clog is within the main drain line, you can't go through the toilet. Either use a water hose or auger through a drain cleanout or down through the vent stack to get rid of the clog before it becomes a full blockage.
Inner Tank Mechanisms
The noises during flushing could originate with the inner mechanisms of the tank, which could simply be doing the job it was designed to do or may be malfunctioning. In a pressure-assisted toilet, for example, a smaller tank within the larger, outer toilet tank thrusts water down through the bowl. This action from the tank's moving parts creates the noise and is the way it is meant to operate. In gravity-fed toilets, a worn fill valve can cause various noises, from screeching to moaning, which indicates the valve should be inspected and either replaced or repaired.