Transliteration is a systematic way to represent the sounds of words in one language using the writing system of another language. The word transliteration is often used interchangeably with transcription. The former is used in modern publications while the latter was used in older publications. (We need a linguist to clarify the differences in definition.) For example, Pinyin is a transliteration system for Mandarin using the Roman alphabet. The same words are likely to be transliterated differently under different systems, for example Peking vs. Beijing. Transliteration can be done in a non-alphabetic language too. For example, in a Beijing Newspaper, president Bush's name is transliterated into two Chinese characters that sounds like "Bu4 Shu1" (布殊) by using the characters that mean cloth and weird.
Transliteration has proven to fail miserably in conveying the original pronunciation. One ancient example is the Sanskrit word Channa which transliterated into the Chinese word Ch'an through buddhist scriptures. Ch'an (禪 zen buddhaism) was translaterated from Japanese to Zen in English. Channa to Zen is quite a change.
The idea of transliteration is complicated by the genuine use in multiple languages of different common nouns for the same person, place or thing. Thus, Muhammad is in common use now in English and Mohammed is less popular, though there are excellent reasons for each transliteration. Muslim and Mohammedan are less interchangeable, but the typical French usage "Musulman" is considered offensively colonialist in English language contexts.
Another complex problem is the adoption of loan words from one language to another, followed by subsequent changes in 'preferred' transliteration. For instance, the word describing a philosophy or religion in China was popularized in English as Tao and given the termination -ism to produce an English word Taoism. That tranliteration reflects the Wade-Giles system. More recent pinyin transliterations produce Dao and Daoism.