A bond futures contract is an agreement on a recognised futures exchange to buy or sell a standard face-value amount of a bond, at an agreed price, for settlement on a standard future delivery date. In some cases, the contract is non-deliverable. In most cases, the contract is based on a notional bond.
The conversion factor, for any particular bond deliverable into a futures contract, is a number by which the bond futures delivery settlement price is multiplied, to arrive at the delivery price for that bond.
The cheapest-to-deliver (CTD) bond is the one which it is most cost-effective for the futures seller to deliver to the buyer if required to do so.