You can advance by place or by prior qualifying performance.
Generally there are three levels, district, region and state.
Each level has qualification performance standard, generally based on a five year rolling avg of prior years results,. At the state level, this is generally based on the 8th place finisher each year.
Usually each team gets 3 entries for each individual event (and one per relay event) at districts which they can fill however they want. If a team has more than three kids that meet the performance standard during that season, they may enter as many as have met the standard.
At districts (and regions) the top x performers (usually 3 or 4) advance by place. Those who have previously met the standard may also enter at the next level (regardless of whether they competed in that event at the prior level).
A team like LV which competes in a midsize school division and has such depth of high performers (relative to the AQ standards) can truly be outliers in this system, having 8-9 entrants in the individual ditance events.