Good question. The anti-dilution right is an adjustment to the investor's shares that occurs when the company does a down-round. The "broad-based" qualifier is a reference to the most company-friendly version of this because it requires the adjustment to take into account the scale of down-round in terms of dilution. For instance, if you closed a round at $20M post and then sold one share afterwards at $10M post, the adjustment would be negligible. There are other variations of anti-dilution adjustments that would ignore such considerations.
The anti-dilution adjustment is generally not something that applies to ordinary course dilution (like employee option grants).
Surely early investors will be diluted, so what are these peculiar rights referring to?