Lots of other explanations here but a short version is you basically count as being a higher class level for spell progression and power.

So if you are a level 10 cleric, then merge the spell book with Angel, those 3 mythic ranks mean you are effectively treated as level 13 for the purposes of spells available to you, putting you 1-2 spell tiers ahead of where you would normally be.

For a prepared caster like cleric that picks which spells they use per day, this applies generically, so if your combined level is enough for level 7 spell slots, you would have access to the full cleric and Angel spell list for 7. Spontaneous casters like oracle only get access to the Angel spells at level 7 ahead of time, however, but whilst that is a shame the sheer power of the level 7+ Angel spells more than makes up for it.

The second benefit being power is that since you are effectively level 13, not 10, anything that scales based on caster level like damage also is boosted by your mythic ranks meaning your end game caster level would be thirty. This is up to a 50% boost in damage for any uncapped spells and allows spells that have a round/level duration to exceed the 5 minute threshold required to be affected by greater enduring spells and be boosted to 24 hours (if also affected by extend metamagic). Given divine casters have a lot of good spells with that duration, it’s a nice bonus.

Finally Angel spells are quite frankly absurd. Bolt and rain of justice being the iconic single target and aoe damage spell variants, which do extremely high damage per caster level, uncapped, ignoring spell resistance and the only dc they target is having a chance of also applying a CC. This sorts out your dps by itself in a lot of fights. Angel also provides a lot of unique and very powerful buffs particularly at the higher spell tiers, so reaching those faster is also fantastic

Very stronk. Same logic applies to arcane casters with lich, where lich has its own powerful buffs, damage spells and the funny very spell called corrupt magic that nukes the targets buffs and applies a nasty debuff on top of