Naturalization: Common term for when someone legally adopts the nationality of a country they are resident in, but were not born in.

aaa Becoming a UK Citizen - Naturalization
aaaNCADC would advise all foreign nationals who have permanent residence in the UK but have not taken out British citizenship, and wish to remain in the UK, to consider becoming a citizen of the UK.

aaa The various forms of leave to remain granted to refugees/asylum seekers\spouses etc, still leave those granted admission on these terms, subject to UK Immigration Controls. Only 'Naturalization', taking out British Citizenship, will give you equal rights with UK citizens, who are not subject to UK immigration laws. NCADC would in particular advise all spouses to take out UK citizenship as soon as possible, this will give them some protection in case the marriage fails.
   
aa Becoming a European Union Citizen! - through Naturalization
    In recent years, more and more British citizens have had to confront the fact that British immigration law gives them no right to live with their family in the UK.
aaaHowever, there may be a way round this, if someone born in the UK, has one or both parents born in another European country, France, Ireland etc. they should be able to become a citizen of that country through 'Naturalization'. They don't have to leave the UK to do this, and adopting the nationality of another EU country, will give them stronger family rights. As they will then be able to  exercise European Community rights of residence in the UK which are much more extensive when it comes to family reunion issues and will in normal circumstances override UK immigration rules. ( see 'The Surinder Singh Route to Family Reunion').     

aaaBelow is the UK Home Office criteria for Naturalization.

aaCitizenship and Naturalization
    Once a person has had indefinite leave to remain for a year they may apply for naturalization as a UK citizen.
    Once a candidate has been physically resident in the UK for a year as a permanent UK resident, they may apply to become a naturalized British citizen. Unfortunately, naturalization applications are likely to take one to one and half years to be processed. Those who seek naturalization other than by marriage to an UK Citizen must meet the requirements outlined below:
General Requirements for UK Citizenship and Naturalization:
aaa* They must be aged 18 or over and are not of unsound mind.
aaa* They must be of good character.
aaa* They should have a sufficient knowledge of the English language (or Welsh or Scottish Gaelic). There are exemptions to this a aaarequirement, for example if one is old or mentally handicapped.
aaa* They should intend to live in the UK or in Crown Service abroad (working directly for an UK Government organisation), or be employed by an international organisation of which the UK is a member, or be employed by a company or association established in the United Kingdom.
    In addition the UK citizenship candidate should have fulfilled the five year requirement as detailed below. The five year period is measured from the five years the date the application reaches the home office.
aaa* The candidate must have been in the United Kingdom at the beginning of the 5 year period; and
aaa* In the 5 year period the candidate must not have been outside the United Kingdom for more than 450 days; and
aaa* In the last 12 months of the five year period the candidate must not have been outside the UK for more than 90 days; and
aaa* In the last 12 months of the five year period the candidate's stay in the United Kingdom must have been not subject to any aaa atime limit under the immigration laws; and
aaa* The candidate must not have been in the United Kingdom in breach of the immigration laws at any time in the 5-year period.
aaa aBritish Nationality by Marriage:

     The requirements are very similar to those mentioned above. The main differences are that there is a shorter residence requirement of three years. As above the relevant residence requirement, being three years in this case is the period ending with the date the application is received by the Home Office. The residence requirements in more detail are as follows:
aaa* The candidate must have been in the United Kingdom at the beginning of the 3 year period; and
aaa* On the date that the candidate's application is received in the Home Office, their stay in the United Kingdom must be not aaa asubject to any time limit under the immigration laws; and
aaa* In the 3 year period the candidate must not have been outside the United Kingdom for more than 270 days; and
aaa* In the last 12 months of the five year period the candidate must not have been outside the UK for more than 90 days; and
aaa* The candidate must not have been in the United Kingdom in breach of the immigration laws at any time in the 3-year period.
    This is a simplification of several complex laws; there may well be other important issues to consider.

Source for  Citizenship and Naturalization:

Visa Application Process