The European Union (consisting of Austria, Belgium, Denmark, Finland, France, Germany, Greece, Ireland, Italy, Luxembourg, Netherlands, Portugal, Spain, Sweden and the United Kingdom) has set up rules for selling certain types of products within the EU. For example, there are rules for medical devices, machines with moving parts, electronic devices, etc. If you want to sell a product in one of these categories anywhere in the European Union, your product must meet the standards set by the rules. If your product meets the standards, it can bear a CE marking and be sold in the EU.
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.
Here are some interesting links: