Signed Exact English (SEE) was developed in 1972 by Gerilee Gustason. It is not a language; it is a manually coded form of English that uses ASL signs supplemented with special signs or inflections that allow English to be signed exactly as it is spoken.
The supplemental items added to SEE, which are handled differently in ASL, include things like pronouns, plurals, possession, and the verb "to be". For example, pronouns are handled via spatial reference in ASL, but would be signed as a specific sign representing (for example, the word "he" or "she") the pronoun in SEE. Also, SEE includes special signs for "is", "are", "was" and other forms of the verb "to be", which are just not used in ASL.
SEE is most often used in an educational setting, where the focus is on English as a first language. It is more likely to be used by deaf people than by Deaf people.
Proponents of SEE believe that it helps with learning English, since it manually reproduces English word-for-word in the same order as English.
There is some controversy over whether someone who needs a manual language would be better off with SEE or with ASL. Proponents of ASL point to the fact that it's possible to become skilled in both English and ASL, without signing in SEE.
It's very much a personal preference. People who are comfortable with ASL would never sign among themselves in SEE even though they could understand and communicate with someone who did sign in SEE.
In practice, people who use SEE often sign in Pidgin Signed English (PSE) rather than "exact" English. PSE is neither ASL nor SEE, but is perhaps best described as a combination of both.
You can learn more about SEE by clicking on the following Google Search string:
"Signed Exact English".
Thanks to Chris Lyons for suggesting this term.