If a company has 1 billion shares but a founder and the state hold 600 million that never trade, only 400 million are investable. A float-adjusted index weights the company on that 400 million, so index funds are not forced to chase shares that do not exist in the market.
Without the adjustment, index trackers would compete for a thin float at every index-reconstitution, driving prices away from the value the index is meant to represent. Float adjustment is now standard at the major providers, though the definitions of strategic holder differ between them.
Float bands also cause silent weight changes: a lock-up expiry or secondary offering can raise a company's index weight without any price move, forcing buying from every tracker. See index-reconstitution for the effects this creates.
Related: index-construction, market-cap-weighted-index, index-reconstitution, float, index-fund, liquidity