Alpha privative is the fancy grammatical term for the prefix a- or an- when used to denote negation in Greek and in English words derived from Greek roots, such as atheist and anesthesia.
The alpha privative is used to express negation, an opposite, or an absence. 'Alpha' in this case refers to the Greek letter ά- (and the form αν-, used before vowels), and hence their Latin and English forms a- and an-. 'Privative' refers to that which deprives.
This is in contrast to the copulative a, which is also a Greek prefix using the letter a- or ha-, which is used to indicate that two things are the same. This has not gained foothold in English.
Modern English has borrowed from other languages that have prefixes that serve the same function as the alpha privative; the Latin in- and Old English had un-.