Conversion Discount
A discount, expressed as a percent, off the price-per-share of the next qualified priced round.
For example:
If the incoming investors of the new series are paying $5/share and convertible note holders have a 20% discount, then the note holders will convert at $5 * (1 - 0.2) which is $4/share.
This is a guaranteed discount against the share price paid by the new investors, the perk of investing earlier and at greater risk.