Actual cash value and replacement cost are two formulas that insurance companies use to calculate how much they will pay you to replace an item you file an insurance claim for. Each insurance company wants to pay you as little money as possible, but you want to get as much money as possible from your insurance company to replace your lost, stolen, or damaged goods.
An insurance company that uses actual cash value to calculate how much your insurance will cover for you is saying that they will pay you the "actual cash value" of your item. In other words, they will give you the original amount of money the item was worth, minus an amount calculated to represent the wear and tear your item has undergone. An insurance company would prefer this option because they would end up giving you less money.
Replacement cost means that the insurance company will give you enough money to replace your item with the same type of item. Pick an insurance quote that gives you this option, because you will end up getting more money from your insurance company.
Think about it this way. If you lose your bike, and your bike was insured by an insurance company that uses actual cash value to calculate how much money they will give you for your insurance claims, then you will receive the money the bike was originally worth, minus an amount for wear and tear. If you have an insurance company that uses a replacement cost formula, you will get money from your insurance company that is equal to the amount necessary to replace your bike.