Asynchronicity sounds like a difficult term, but it simply is an indication of action and time. Asynchronous events do not necessarily occur at the same time. They might have to wait or listen for other events to happen. To understand what asynchronicity exactly is, it is probably better to look at examples from everyday life. As a matter of fact, real life is full of asynchronous events.
Imagine you are meeting up with two friends for dinner. You take the tram to arrive from point A to the restaurant but have to make a stop halfway to run some errands first. Your friend is taking the tram half an hour later from the same starting point but arrives at the restaurant before you do; she did not have to stop halfway. She then notifies the third of the company, who waiting nearby, arrives immediately. When you arrive theyare already having a second round and waiting to order food. You have to notify the waiter.
Read also the example in the article below
Taking the examples from real life, how is asynchronicity introduced in programming languages?
Read the articles
Polymer: Dealing with asynchronous tasks
Polymer: Delaying work
Tutorial savvy: Use of Polymer async method