Minimum is the smallest bid amount that you will entertain as an offer.
If I say there is a minimum of $250 - it means dont bother bidding below $250 on the domain.
Reserve is a price that is hidden from potential bidders (usually). It is the price that you will sell at. For Instance on Sedo, if there is an auction with a reserve, the auction bidding must surpass or equal the reserve in order for the sale to be complete. If it doesnt meet the reserve there is no sale.
Asking price is typically a high end number that a buyer will suggest for selling the domain name for. Usually a asking price is inflated because the seller is expecting to negotiate with a potential buyer.
If you want to sell a domain name for a minimum of 5k - a reasonable asking price might be 8k. However when someone uses the word "firm" with their asking price, it means they will not accept less.
Hope this helps!
Justin