What is it called when a word is translated phonetically from a foreign language to English?

That practice is called transcription:

1.2 A form in which a speech sound or a foreign character is represented:

ODO

Transliteration is not necessarily a phonetic operation:

Transliterate:

Write or print (a letter or word) using the closest corresponding letters of a different alphabet or language:

ODO

Because Arabic has a dissimilar alphabet system, جهاد‎ ǧihād [dʒiˈhæːd] comes across as a phonetic transliteration, which is technically transcription.

There are specific principles of transcription applied to each language separatey.

• http://en.wikipedia.org/wiki/Romanization_of_Arabic
• http://en.wikipedia.org/wiki/Romanization_of_Hebrew
• http://en.wikipedia.org/wiki/Romanization_of_Japanese
• http://en.wikipedia.org/wiki/Romanization_of_Russian