Don't know, it depends on data structure. In the multilevel framework, multiple observations can be clustered (repeat measures) in a unit (e.g., person, state, classroom). So the random intercept and slope means that those parameters can vary by unit (person, state, classroom) level. One underlying reason is that a person's y-values have a covariance structure, if I have a lab value of say 37%, the next month's values will likely not be independent of the previous month's value.
Thanks for your reply. In my case multiple observations are nested in each person. So, if I have understood correctly so far, random intercept means that each person has different intercept (meaning different value on y, when x is 0), and random slope that there is different effect of x on y for each individual?