It is a fun holiday but it has a real and necessary purpose.
Like much else mechanical, dirt, smoke, dust and pet hair can damage your computer. In a computer generally, the problem is two-fold
1) These products settle on your computer components and as they are an insulator act as a blanket and making the computer run hotter then it is designed to run. What this does is reduce its life expectancy and cause parts of your computer like the memory, the processor and the power supply to misbehaviour or stop working. I have seen several short circuits of delicate electrical components caused by dust too generally in the CD and DVDs.
As a rule, try to put a computer in a clean location, near a fireplace, where your dog sits on, dusty place, etc is not suggested.
In an effort to overcome the heat what the computer does is push the fan to run faster which can cause the fan to break from overuse which brings us to the second problem
2) The computer has several moving parts and vents mainly in the ventilation system. The dust, hair etc can reduce the ventilation system efficiency. If enough cold air cannot come in then the computer is going to run hot. If they jam the fan they can break it too.
As a rule, try to put a computer in a spot where its air vent has access to cold airflow. Next to heating vent is not suggested.
Now, what can you do about the dust already in the computer?
If you have seen the movie Zoolander and this is you on the computer mechanics, now stop reading and ask someone else to help out.
Here is a video that I do suggest the person cleaning your computer views first and remember there is a good reason why this holiday was set up on a Monday if something goes wrong on a weekday you can get professional help if something goes really wrong.