When a Dynamic Pricing Mint goes live, the price to mint will start at a certain level and keep dropping until someone starts minting, after which price will continue rising as more and more people choose to mint. If demand tapers off, then price will drop again until more demand kicks in. As such, the price will keep moving upwards and downwards depending on demand, which is why it's called dynamic. Dynamic Pricing Mint on Magic Eden Launchpad will be powered by Strata Protocol, and you can read more about how it works here.
Let's see look at a few examples on how this works in practice. In the screenshot below, you can see the mint started at 0.24 SOL and dropped to around 0.10 SOL. Demand kept steady at 0.10 SOL for 5 days until the very end of the chart where we can see it tick upwards slightly to 0.11 SOL, which means demand increased at the very last minute -- perhaps a few people waited 5 days and then all started minting at the same time.
Because of the way dynamic pricing works, it is possible for the final minting price to be higher than the starting price if demand ramps up heavily towards the end of the minting period. Waiting too long to mint could cost you more, and timing your mint well could help you avoid the top minting price, too, as you will also see in the below example:
We can also see that each stage has its own dynamic pricing, with the first stage "whitelist presale 1" ending at average 205.39 SOL, and the the second stage "whitelist presale 2" currently at 394.17 SOL. Each stage will have its own starting price set by the collection.
Note: the price you end up paying might be ~10% higher than what is shown on the screen due to a preconfigured slippage -- you can think of this is a tolerance margin. This slippage accounts for periods when the price is rapidly changing, i.e., between the time you pressed "Mint" and the time the transaction is finalized, the dynamic mint price may have already moved slightly.
If you'd like to learn more about the underlying technology and pricing curves being used, you can read more about Strata Protocol's Dynamic Pricing Mints here.