What is the exact meaning of Load?
Load is the generic term for something in the circuit that will draw power.  The characteristics of a "Load" can vary widely.  It is normally the largest power draw and most components in the circuit are there to support the Load.  Anything that uses electricity to do work will draw current.  The amount depends on how much resistance to current flow the device has and the amount of voltage applied to it, assuming the source has more power to give than the load will use.

The term is derived from a physical load, like carrying a bundle of wood.  It requires work, when you are loaded down.

In your question about an air conditioner, you are running into non-simple loads.  A large electric motor will behave differently at startup vs when it is running normally.  An air conditioner has a fairly high load running the compressor.  Imagine a car starting out from a stop, there is more energy needed to get it moving than keep it moving.  This is the same with a motor and there is an inrush of current to get it moving.  This is either due to starting coils, which are switched out when the motor is at speed, or changing electrical characteristics of the motor between stopped and running mode.

The reason your lights dim are because the extra current draw causes the house wiring to the AC unit to lose more voltage before it gets there.  (Look up Ohm's Law and compare fixed resistance with varying current.)  Once the initial inrush of current is over, the voltage drop subsides and the lights resume their normal power.