Simply, your museum is where you put your old ships that you don't / won't use again, ie. Le Grace. Once you place them you can never remove them for use again so be thoughtful of which ones you put in there. Then once they are in there, they produce income per boat. Doesn't matter how big or small of a boat, the income is based on the number of boats in there. You get a certain amount per hour per boat up to its cap. You collect this income anytime a coin hovers over top. Now keep in mind, the amount you get is based on a per hour basis however, you will get a hovering coin more often than this and the amount is smaller. It adds up the same as if you were to wait the full hour. Similar to the fishing boats when you collect fish every 20 seconds, it adds up to the hour amount. Anyways, the museum is good for old dead boats to declutter your dry dock. Here is a link to explain the income...
http://seaporthelp.i-host.hu/eng/epuletek.php#museum