CE stands for Conformité Européenne, which is French for "European Conformity." A product in one of the controlled product categories cannot legally be sold in the EU unless it has passed the tests to receive the CE marking.
For a company trying to sell a product, getting a CE marking makes things much easier because it means you can sell the product anywhere in the EU. In the United States, electronic device manufacturers need to meet the same sort of requirements to get FCC approval.
