In my experience, to understand something like Threads/Parallel computing in this case, i always come from "Real life".
Like this morning:
I entered my car, and started it.
After getting my morning coffee at the local gas-station i continued driving on towards my workplace.
Once driving again (one Process/Thread), i turned on the music in my car (launching a second Thread/Process).
Some minutes later while waiting at a red light, i lit a cigarette (Yes, i smoke in the car) (launching a third Thread/Process)
Bottom line: As described above, there are three distinct "Processes" happening at the same time
Or let's take driving only.
When you drive a car, and you want to switch lanes, you hit your direction indicator, because your Thread "driving" received a message "You have to get to the other lane, because you want to use the next exit".
This is happening WHILE you're still driving. It's not like you stop driving, hit the indicator, and then start driving again.
The human brain itself is a marvel of "parallel computing", though many women will argue that males are not capable of "multi-Tasking" :-)
EDIT: Or to use another analogy:
1) Breaking up a big problem into smaller parts
Imagine a big Open-Air-Show moving from one venue to the next. What do they do?
They load up the whole Production (="One Big Problem" --> Stage, Lighting, Speakers, Instruments) into separate, multiple Trucks, wherein each Truck has its own "Load" ("smaller Problems")
They drive in "parallel" (think "Convoy") from Point A to Point B. The "Big Problem" is "solved" when each Truck arrives at their destination (Note: Not neccessarily at the same time)
2) Parallel Processes passing messages
Take a Football-Team. You have 11 Threads/Processes running at the same time.
The left defender "passes" the ball to the right Midfielder, and sending this Midfielder the Message "Pass the ball back to me because i will be running forwards along the sideline" --> synchronous! It doesn't make sense for the right Midfielder to pass the Ball back, if the left Defender has'nt arrived at his intended Destination.
Now the left defender has gotten the ball back, and shoots a pass blindly into the penalty box in front of the goal --> asynchronous! The left defender passed the Message: "I'm done. Do with it whatever you want"