A system of Japanese romanization that emphasizes consistency with the actual Japanese phonology rather than imitating the correct pronunciation with the Roman alphabet. Simply put, JSL basically makes each kana character equivalent to a particular syllable in English, whether or not that syllable represents the actual pronunciation. The idea is more to form an intermediate step between English and written Japanese than to make the pronunciations exact. This contrasts with the more familiar Hepburn system, which goes for easy pronunciation over linguistics.

For an example of the differences, take the romanization of a Japanese sentence in JSL versus the Hepburn equivalent:

Kyoo ame ga huru desyoo. (JSL)
Kyõ; ame ga furu deshõ (Hepburn)
It will probably rain today.

Why use the more confusing JSL system, then? The advantages of JSL can be illustrated by the following. Suppose you are using the Hepburn system, and you want to form the stems of the following consonant verbs:

kau --> kai (buy)
matsu --> machi (wait)
hanasu --> hanashi (speak)
kaku --> kaki (write)

You'd have to describe the procedure as the following:

Change the final u to i, but if u is preceded by ts, change ts to ch, and if u is preceded by s, add h after the s.

Look at the same thing written in JSL:

kau --> kai
matu --> mati
hanasu --> hanasi
kaku --> kaki

You can now just say "Change the final u to i." Much simpler, and more consistent. Matsu (Hepburn) and Matu (JSL) are both pronounced the same, and therein lies the problem. To use JSL, you need to know that the JSL representation "tu" is actually pronounced "tsu", with the "ts" as in "cats". Hepburn, however, requires no foreknowledge of Japanese phonology. JSL is often used in Japanese textbooks, as it makes discussing and teaching the language much easier, but Hepburn or some hybrid is found almost everywhere else, including anime subtitles, dictionaries, and quotations in English writing.