A conversion ratio, in the context of investment, means the number of units of the underlying that will obtained for each unit of a derivative (which includes embedded derivatives, as in convertible bonds. The term has other meanings in other contexts.
For a convertible bond the conversion ratio equals the par value of the bond divided by the conversion price (the share price at which conversion takes place)
The conversion ratio (unless it is one) also needs to be included in other calculations. For example the gearing of a warrant (the fractional rate of variation of its intrinsic value with the fractional change in price of the underlying) is:
price of underlying ÷ (price of warrant × conversion ratio)
The gearing is often adjusted using delta to give effective gearing.