Translation is the comprehension of the meaning of a text and the subsequent production of an equivalent text, likewise called a "translation," that communicates the same message in another language. The text that is translated is called the source text, and the language that it is translated into is called the target language. The product is sometimes called the target text.
Translation, when practiced by relatively bilingual individuals but especially when by persons with limited proficiency in one or both languages, involves a risk of spilling-over of idioms and usages from the source language into the target language. On the other hand, inter-linguistic spillages have also served the useful purpose of importing calques and loanwords from a source language into a target language that had previously lacked a concept or a convenient expression for the concept. Translators and interpreters have thus played an important role in the evolution of languages and cultures.
However, localization and internationalization is not separated, which I think they should be. Here is the joint definition:
In computing, internationalization and localization (also spelled internationalisation and localisation, see spelling differences) are means of adapting computer software to different languages and regional differences. Internationalization is the process of designing a software application so that it can be adapted to various languages and regions without engineering changes. Localization is the process of adapting internationalized software for a specific region or language by adding locale-specific components and translating text.
The terms are frequently abbreviated to the numeronym i18n (where 18 stands for the number of letters between the first i and last n in internationalization, a usage coined at DEC in the 1970s or 80s) and L10n respectively, due to the length of the words. The capital L in L10n helps to distinguish it from the lowercase i in i18n
Some companies, like Microsoft, IBM and Sun Microsystems, use the term "globalization" for the combination of internationalization and localization. Globalization can also be abbreviated to g11n.
Lionbridge has a good explanation of the difference between the two:
Internationalization readies your product for global markets and ensures it can be localized easily. It is the designing and re-engineering of a product so that it can be localize easily for global markets. It is important to complete internationalization before localization begins; otherwise, you may need to reengineer your product in parallel with localization.
Transcreation is perhaps such a new word that Wikipedia has no definition yet. Here is one definition I found:
Transcreation: Adaptation, mainly used in drama contexts, is defined as “the ‘freest’ form of translation” and one where “... the SL [source language] culture [is] converted to the TL [target language] culture and the text rewritten” (p. 46).The idea of rewriting a text to adapt it to the norms of the target culture, to the point that little trace is left of its source, seems to be at the root of transcreation, too. Nowadays often used in advertising and the media, transcreation is a portmanteau word made by combining together translation and creation, in order to emphasise the considerable amount of creativity required in the process. (From http://www.airy-eel.blogspot.com)