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SERIAL DILUTION

means doing your dilution in several steps, instead of all at once.

So instead of taking 1 mL of your 1 M stock solution and making a liter of your working solution in one step, you might...

take that 1 mL of stock solution and add it to 9 mL of water. Now you have a more dilute stock solution to work with! The new solution will only be 0.1 M.

If you took 1 mL of this new solution and added it to 9 mL of water, you would get a 0.01M solution.

Then if you took 1 mL of that and added it to 9 mL of water, you would get the 0.001M, or 1 mM solution you wanted! And you would only have made 10 mL of it, not a whole liter.