As you explained, Inception is an event that is a beginning; a first part or stage of subsequent events.
In this movie, lead protagonist Dominic Cobb(Leonardo DiCaprio) has got a task to implant an idea into Robert Fischer's subconscious mind by going into his dream. And that person will have a life and act according to what has been implanted into his mind.
Therefore, in this case, inception is just an activity to plant an idea into someone else's brain to start a chain of events.inception is just an activity to plant an idea into someone else's brain to start a chain of events.