'
Hay' is an irregular, or special, conjugation of the auxiliary verb
haber, in the present tense. This conjugation is translated into English as 'there is' or 'there are.'
The regular third-person conjugation of
haber is '
ha' (singular) or '
han' (plural). This conjugation is translated into English as 'has' or 'have,' and this auxiliary is used to form the present perfect tense. In Spanish, the perfect tenses are called the compound tenses.
Here's a
video, mostly in Spanish, that explains the three irregular conjugations of '
haber,' used to convey the idea of 'existence' or 'sudden occurrence.'