# Understanding the meaning of $U^I_{ijp}=X_{jp}\beta^I_{i}+\epsilon^I_{ijp}$

I am currently looking into the following research paper:

(1) In the equation $$U^I_{ijp}=X_{jp}\beta^I_{i}+\epsilon^I_{ijp}$$ I understand that $$X_{jp}\beta^I_{i}$$ provides the required linear combination, but what is the relevance of adding $$\epsilon^I_{ijp}$$ to it? (Is it the error term? Why do we need it?)
Moreover, it is mentioned that "$$\epsilon^I_{ijp}$$ follows an independent and identically distributed standard normal distribution that implies a multinomial probit model of choice". I definitely don't comprehend this part and need some help here.
(2) Another source of confusion for me is the line on the same page that reads "Consumer-specific attribute importance weights are allowed to vary across consumers, and to be correlated across attributes, as follows:"$$\beta^I_{ik}\sim N\big(\bar\beta,\Sigma\big)$$