Persona
Meet Carlos.

He is an academic course-coordinator in a university. He is a very busy man who spends most of the day in front of his computer.
User Observation
As Carlos goes on about his daily tasks, every half an hour or so he checks the time. Reasons vary:
- How long has he got before the 11:00 meeting?
- How long before lunch time?
- How long has he been replying to emails?
- How long before I go home?
In the specific day you observed Carlos, he checked the time 21 times. He spent 6 hours and 42 minutes in front of his computer screen.
As you observe Carlos, you see that in order to check the time he uses his iPhone instead of his watch. When asked why he replies:
"Because my iPhone clock is automatically synced to a time server and thus it is more accurate than my watch."
You further observe that behind Carlos there's a wall clock stuck on 2:40. You ask Carlos why the clock isn't working.
"It ran out of batteries 2 weeks ago and no one is asked to replace them."
A Revolutionary Design
And then you have a moment of enlightenment:
How about we save Carlos the need to reach his pocket, fetch the phone, look at the time and put the phone back in his pocket. How about:
- We provide Carlos with a small clock in the top bar of his screen (which he looks at most of the day anyway), so he only needs to move his eyes to see the time?
- Not only this, but the desktop clock will also be synced to a time server (the machine is connected to the internet anyway), providing Carlos with the most accurate time.
- In addition, how about clicking on the clock will reveal date information (which Carlos checks less regularly)?
You propose it to Carlos and he thinks it is a genius idea. He goes about how it can save the need to buy, maintain (batteries), and calibrate wall clocks on all rooms which have computers in them.
This is User Centred Design.
Conclusion
People often check the time (user need), and if in front of a computer (context), a small clock on the screen (design solution) is the quickest and most accurate way for them to do so.
Run an observation on many different personas and you'll find the same applies.