Naturalization simply means giving an immigrant to a nation the rights and privleges of being a natural born citizen, in a nutshell this is called citizenship. A naturalized person is considered to be a citizen of the nation that has granted him naturalized status. This gives him all leagal and voting rights that would automatically be given to someone born in a country.
In most countries, naturilization generally means that a person has met the basic requirements to be considered for naturalization. They usually are that the person has held a legal status as a full-time resident in the country for a minimum period. They also must promise that they will obey and uphold that country’s laws. This us usulaly done with an ceremonial oath or pledge of allegiance.
There are some countries that require a naturalized citizen to renounce any other citizenship in a nation that he currently holds, thus forbidding dual citizenship. However, whether or not this renunciation actually causes a person to lose his original citizenship depends on the laws of the respective countries involved.
Every country has a different system for applying for natualization and eventually the Global Citizen Project will provide this information freely to the whole world.