I'm going to assume you're referring to the version of Balazar that comes in the Wrath of the Righteous base set because you list his power as discard a spell to draw a random monster from the box, whereas the class deck version of Balazar has a similar power allowing him to recharge a spell to do so.
Does this mean I have to encounter the monster also or do I just get to keep it?
You just draw it - no encounter.
The first important thing to recognize is that Balazar has a Cohort, his eidolon Padrig. (Cohorts are listed on the back side of a character card by their deck list.) Balazar is expected to use his eidolon to fight, especially since he doesn't get to keep offensive spells (those with the Attack trait) after playing them.
Display this card. While displayed, when you attempt a Strength check and do not play a weapon, you may put a card on top of your deck to add your Arcane skill plus the scenario's adventure deck number to that check. You may banish any number of monsters; for each monster banished, add 1d4 to the check, or 1d6 if you have a role card. If you are encountering a monster, add another 1d6 for each monster banished that shares a trait other than Basic or Elite with the monster you are encountering.
So, you add Padrig to your starting hand after drawing your hand size. You'll display him once the first turn begins. Thereafter, for combat, you will roll your Strength (1d6), since Strength or Melee is always allowed for combat, then use Padrig's power to put a card from your hand on top of your deck to add your Arcane skill (1d10+2 initially) plus the level of the scenario you're playing (so the power scales up at higher levels). Next. you can banish any of the monsters from your hand to add 1d4 for each you banish (1d6 once you have a role card) plus another 1d6 for any traits the banished monster shares with the the monster you are encountering. Fighting a card with the Demon trait? Banish a monster from your hand with the Demon trait to add 1d4+1d6, or 2d6 if you have a role card. Then, if you win your combat, you can just add that Demon monster you just defeated to your hand, and you're ready for the next one you face!
If I were playing Balazar, I'd try to have a couple monsters in my hand most of the time. If I know what traits the henchmen or villain have, I might prioritize keeping a monster with a matching trait for what I'd expect to be a tougher fight.
Once Balazar gets a role, he has even more ways to use monsters from his hand - adding 1d4 to any check to defeat a barrier, to acquire certain types of boons, etc. The Tyrannomancer can even get a power allowing him to banish monsters from his discard pile to use some of these additional powers. Granted, his combat power still uses monsters from his hand, but maybe you discarded a monster or two as damage at some point, or just to draw some different cards. Then you can use those discarded monsters for these utility powers and save the ones in your hand for combat.
Meanwhile, the Eidolomancer can gain a power letting him use Strength for his Constitution/Fortitude checks, or Dexterity/Stealth checks with another power feat. Now, if you have to make a Fortitude check, you can choose to use Strength, then banish a monster from your hand to use Padrig's power to add your Arcane skill plus the scenario's level plus 1d4/1d6 for each monster. Great versatility, and he can get really good at multiple skills!
One more note: being able to "trade" any spell for a monster (which at later levels will provide more options than most spells) means Balazar will always be happy to encounter spells when exploring, even if they aren't spells he's interested in casting.
That's what I could think of off the top of my head. I hope it helps. Please let us know if you still have questions!
The Summoner class in this game is so cool. Probably my favorite Class Deck.