When offering convertible debt, the investor accepts the valuation at the next round of investments (in this case series A).
The risk for the convertible debt investor is that this valuation will be very high and the series A can take a long time.
To limit this risk convertible debt investors negotiate valuation caps and discounts.
Cap: The convertible debt gets converted at min=[series A valuation, cap].
Discount: The convertible debt gets converted at series A valuation * (1- discount)
(Obviously, when both cap and discount apply, the valuation for conversion becomes min = [series A valuation * (1 - discount), cap].)