I am an accounting student in the last semester, hold some business diplomas and have many years of business experience. I doubt that a 3 year old wants to know the difference about fixed and variables, but I will try my best to stay on earth.
As the terms already imply cost is fixed (always the same) while the other varies (different depending on the quantity produced).
The variable cost depends on the quantity of units produced in order to change. For instance, in order to run a business it is required to pay: rent, office cleaning, office/sale employees, etc; all these cost do not change regardless how much this business produces, whether the business manufactures 100 or 1mil items. Therefore, in business we call this a FIXED COST.
Now, to manufacture, for instance, a bed it requires bolts, nuts, screws and timber panels and so on. All these items when purchased are considered to be a cost to manufacture a bad. Of course, the more beds the business produces the more bolts, nuts, screws and timber panels are required. Hence, these costs change accordingly to the quantity of goods (beds) produces. As this cost varies depending on the quantity produced, it is called VARIABLE COST.
Understand that this is a really simple example and even with this simple bed production scenario it can go more complex. Variable cost is also found in items that do not seem to change depending on production. For example, one may say that electricity cost is always the same and therefore a fixed cost, but this is incorrect. The more holes are drilled into a timber panel the more often the worker uses his drilling machine and requires electricity. But the office light and the light to illuminate the advertising in front of the company runs day and night and does not change regardless how many beds are produced. So, we see that the electricity bill will have some FIXED COSTS AND SOME VARIABLE COSTS INCLUDED. The managerial accountant will calculate how much is accountable for fix costs and variable cost and will account for these amounts only in his financial records / books of accounts (bookkeeping).
The reason why we distinguish between fixed and variable costs is that we can calculate the cost of production and operating cost more accurately. This will then be used to run the business more productively. Decision how to increase production the most efficient way, lower cost, which product line to eliminate, whether we should save on electricity cost when using the advertising lighting, etc.