Asynchronous vs Synchronous execution, what does it really mean?

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When you execute something synchronously, you wait for it to finish before moving on to another task. When you execute something asynchronously, you can move on to another task before it finishes.
In Synchronous program execution, your program is executed line by line, one line at a time. Each time a function is called, program execution waits until that function returns before continuing to the next line of code.

In solving many engineering problems, the software is designed to split up the overall problem into multiple individual tasks and then execute them asynchronously. For example, In computing, sorting a list is an example. The quicksort routine, for example, splits the list into two lists and sorts each of them by calling itself recursively.

Real life example:

SYNCHRONOUS
You are in a queue to get a movie ticket. You cannot get one until everybody in front of you gets one, and the same applies to the people queued behind you.

ASYNCHRONOUS
You are in a restaurant with many other people. You order your food. Other people can also order their food, they don't have to wait for your food to be cooked and served to you before they can order. In the kitchen, restaurant workers are continuously cooking, serving, and taking orders. People will get their food served as soon as it is cooked.

Ref:
https://stackoverflow.com
https://www.bisque.com