How does the at-large system allow voters to choose from a broader base of candidates compared to district system?

To answer this, just think about it in terms of the size
of population available in each case.

If you have a
district system, the only candidates that the voters in a given district have to choose
from are people residing in that district.  This means that there is a relatively small
group of people from which the candidates can come.

But now
think of an at-large system.  In this system, candidates from the whole city or the
whole state are eligible to run.  This gives a much bigger pool of candidates to choose
from.

An at-large system also gives you a broader set of
candidates in terms of ethnicity and ideology.  Where I live, there are very few
liberals.  On the other side of the state, there are very few conservatives.  In
district races, we are stuck with conservatives and the people on the other side are
stuck with liberals.  In at-large races, there are more choices for the people in both
parts of the state.