The share of eligible Search impressions an ad missed because its Ad Rank was too low.
When your ad could have shown and didn't, Google Ads gives two reasons in two columns. Search lost IS (budget) is the share missed because the budget ran out. Search lost IS (rank) is the share missed because the ad's Ad Rank was too low: the bid, the quality or the competition in that auction kept it off the page. Google's API reports anything above 90% as 90.01%.
Together with impression share they add up to the whole: shown, lost to budget, lost to rank. On a brand campaign, lost to rank should be close to zero, because your ad is the most relevant answer to your own name.
So a rise is worth a look. If Search lost IS (rank) climbs on your exact brand keywords while your average CPC rises and nothing in Change history is yours, another advertiser is probably competing harder on your name. Google also reports lost impression share for the top of the page and the very first place, which tell you whether you're losing the top spot rather than the page.
Read it by week, beside Auction insights for the same weeks, to see which domain arrived when the share moved.
Google's own help and policy pages first.