Here is my stab at explaining this issue someone untrained. Of course, I am saying things that most of the readers of this forum already know
The flickering that you are noticing is to be expected, and is _always_ present to a greater or lesser extent in an electrical system. Depending upon the characteristics of the particular electrical system, the flicker may not be perceptible. This sort of flicker can be diagnostic of problems, or it may simply be part of the normal operating aspect of your electrical system. In cases where this flicker is normal for your electrical system, 'fixing' it can be quite expensive, essentially involving replacing the entire electrical supply to your home...and this fix will _not_ eliminate the flicker, but will only reduce the magnitude of the flicker.
All electrical components used in your home will _resist_ the flow of electricity. This resistance reveals itself as a reduction in the supply voltage available to your home when the electrical load increases. In essence, when you use more electricity, a bit gets wasted in the wires coming to your home, and the voltage available to run your lamps decreases. Resistance is present in the normal wires to your house, properly connected. The transformer supplying your house also has its own resistance. If the transformer is undersized for the loads, then the resistance might be excessive. (I wouldn't bother trying to explain the difference between resistance and impedance; for the purpose of this discussion they are the same.) Finally, any bad connections will introduce resistance. It is because of the danger of a bad connection that I will analyze your electrical system to determine if the flicker that you are seeing is consistent with safe and normal operation.
These same rules of resistance apply to individual circuits within your home, however the effects much more pronounced on the circuits involved. You may notice this if you have a high power vacuum cleaner or window air conditioner.
Motors, such as are used in the compressors of air conditioners, consume a tremendous amount of power on startup. This power consumption will cause the voltage drop described above, but only for the instant of startup. This is why motor loads will often cause lights to flicker.
As mentioned above, the voltage drop associated with a motor starting, and the light flicker associated with that voltage drop, can either be totally normal and acceptable from a safety point of view, or indicative of a problem. The only way to know for certain is for me to measure the voltage drop and the current flow, and to calculate the resistance of the supply circuit. I can then calculate the expected voltage drop, and tell you if what you are seeing is normal for your particular electrical system.
If I find excessive unexpected voltage drop, then I can locate the damaged part of the circuit and make repairs. If I find that the transformer is undersized, then I can call the power company and inform them of this fact, although they may not do anything if the transformer seems to work. If the 'offending' air conditioner is on a circuit that is shared with the flickering lights, then I can install a new circuit for the air conditioner. Finally, if the air conditioner seems to be consuming too much power on startup, I can recommend that you call a qualified HVAC technician to evaluate your unit. Finally, if I determine that the voltage drop that you are seeing is within the expected value for your particular electrical system, I can discuss with you upgrades that will reduce the voltage drop and light flicker.
Should you even notice a sudden change in the magnitude of the flicker, or if any of your lights flicker _brighter_ for a moment when a motor starts, this almost certainly indicates a problem that will need to be fixed. In this case, contact me immediately.