Mastering slots available by class level here means that you can master this many spells at this level. In other words, this list only shows the potential number of spells you can learn by any class level, and not any specific spell that you can master or that you earn via any class specializations (heritages/bloodlines, etc.) or slots gained via feats. You must still choose what spells to master yourself via <master level X>, or <spells CLASS>.

Multiclassing will only reflect the level that you reached to in that class. So, if you played a mage for 10 levels and then took 20 levels of fighter, your available slots are for level 10, despite your character being level 30. Some prestige classes, however, will allow you to continue earning spells that match your level. So, your mage 10/fighter 20 takes 10 levels in archmage, you are now a level 40 character: mage 10/fighter 20/archmage 10. Your spells available will reach level 20. First, 10 from your mage class, and then an additional 10 from your archmage prestige class.

Single class spellcasters that take a magic-oriented prestige class will usually choose prestige classes that will continue to earn them more spells by level. A level 40 mage taking archmage gets mage slots up to 50, same as a level 50 mage. However, archmage gets several feats that a level 50 mage does not. To learn more about prestige classes and multiclassing, please look at classes.

Note: Certain classes don't master and therefore are not on this list. Those classes are: druid, ranger, paladin, and cleric.