Allocative efficiency means P=MC

One of the basic conditions of economic efficiency is allocative efficiency. The oft cited condition for this is P=MC. While it is hardly difficult to understand the condition behind productive efficiency (P= min. AC), it is a little more perplexing to think how allocative efficiency can be achieved at P=MC. Interestingly, my teacher actually told me to just learn the condition without going into a lot of details but what I could surmise with my limited knowledge was that since the price we attach with a good is a measure of value we put on a good, if a consumer does not want more of a certain good, it means he puts more value to the good. Thus, if P=MC, we are just paying the price we attach to the good and firms extra cost of producing that goods equals the valu consumers attach to it. Maybe anybody could elaborate on this topic?