Actual Cash Value: Takes into account depreciation, meaning the insurance company will basically give you the used value for your item.
Replacement Cost: The insurance company will reimburse you for the value to replace your item with a new item (up to your policy limits).
Example: Say you purchased a TV in 2010 that was worth $2,000 back then, but now it's only worth $500 (technology prices decrease fast, think about it!), if you had actual cash value the insurance company would reimburse you only $500, where as if you had replacement cost the company would pay out the full $2,000 to purchase a brand new TV. However keep in mind that the insurance will only cover up to your policy limits, if you have $25,000 of coverage and suffer $30,000 in losses, the insurance company would only pay out up to $25,000.
So which should I choose? We always recommend getting the replacement cost option on all of your insurance policies where it is applicable. The slight increase in premium cost is worth it in the long run. In fact if you have a policy with our agency it's likely that you already have the replacement cost option.