if you want to get an idea of what the prices mean you need to take a look in the price indexer.
There are 5 price indexers (even more if you are on enterprise) by default depending on the product type.
Mage_Catalog_Model_Resource_Product_Indexer_Price_Default for simple and virtual products
Mage_Catalog_Model_Resource_Product_Indexer_Price_Grouped - for grouped products
Mage_Catalog_Model_Resource_Product_Indexer_Price_Configurable - for configurable products
Mage_Bundle_Model_Resource_Indexer_Price for bundle products
Mage_Downloadable_Model_Resource_Indexer_Price for downloadable products
The code may look scary but if you sit down and try to understand eventually you will.
the idea is this.
For simple and virtual products there is no different between price, min_price and max_price. See this code in the default indexer:
'price' => $finalPrice,
'min_price' => $finalPrice,
'max_price' => $finalPrice,
But for the rest of the product types there may be differences depending on the products that come into play.
The minimum price is the one that you have to pay to get the product with no additional features. Imagine buying a car. You have the standard price when the car has nothing special on it. but by adding features the price increases until you get to the full option price (that's the max price).