Pidgin Signed English (PSE) is a combination of American Sign Language (ASL) and English.
ASL is a distinct language, and (like most other languages) it does not map perfectly to English. There is no equivalent for many specific words and the syntax is completely different. Culturally Deaf people, signing with each other, usually use ASL, but many people, (frequently deaf or hard of hearing) who learn to sign later in life, after hearing and using spoken English, do not sign strictly in ASL. Instead, they use a mixture of ASL and English that is known as PSE.
With PSE, someone might sign most of the English words of a sentence and use approximately the English syntax.
PSE is not Signed Exact English (SEE), which uses signs for exact English words (even signs that don't exist in ASL) and exact English word order. SEE is most frequently used in educational settings, where the theory is it will help the children learn English. PSE is most frequently used by people whose primary language is spoken English.
Culturally Deaf people are usually very adept at understanding and using this blend of English and ASL when they sign with someone who doesn't strictly use ASL.