Transliteration is a type of conversion of a text from one script to another that involves swapping letters (thus trans- + liter-) in predictable ways (such as α → a, д → d, χ → ch, ն → n or æ → ae).
For instance, for the Modern Greek term "Ελληνική Δημοκρατία", which is usually translated as "Hellenic Republic", the usual transliteration to Latin script is "Ellēnikḗ Dēmokratía", and the name for Russia in Cyrillic script, "Россия", is usually transliterated as "Rossiya".
Transliteration is not primarily concerned with representing the sounds of the original but rather with representing the characters, ideally accurately and unambiguously. Thus, in the above example, λλ is transliterated as 'll', but pronounced /l/; Δ is transliterated as 'D', but pronounced /ð/; and η is transliterated as 'ē', though it is pronounced /i/ (exactly like ι) and is not long.
Conversely, transcription notes the sounds but not necessarily the spelling. So "Ελληνική Δημοκρατία" could be transcribed as "elinikí ðimokratía", which does not specify which of the /i/ sounds are written as η and which as ι.
Systematic transliteration is a mapping from one system of writing into another, typically grapheme to grapheme. Most transliteration systems are one-to-one, so a reader who knows the system can reconstruct the original spelling.
Transliteration is opposed to transcription, which maps the sounds of one language into a writing system. Still, most systems of transliteration map the letters of the source script to letters pronounced similarly in the target script, for some specific pair of source and target language. If the relations between letters and sounds are similar in both languages, a transliteration may be very close to a transcription. In practice, there are some mixed transliteration/transcription systems that transliterate a part of the original script and transcribe the rest.
For many script pairs, there is one or more standard transliteration systems. However, unsystematic transliteration is common.