Oppressive lane pressure and poke.
Empowered abilities and resource manipulation
Hitting a champion with spells hurls a comet that deals adaptive damage at them. Landing more spells reduces Arcane Comet's cooldown.
Hitting enemy champions with a spell grants maximum mana.
After reaching 250 mana, Manaflow Band restores 1% of your missing mana every 5 seconds.
Gain 10% CDR when you reach level 10. Excess CDR becomes AP or AD, Adaptive.
Your first ability hit every 20s burns champions.
+20 Ability Power or +12 Attack Damage, Adaptive
You get free boots at 10 min. but you cannot buy boots before then. These boots give additional MS. For each takedown you acquire the boots 30s sooner.
Get a free biscuit every 3 minutes, until 12 minutes. Biscuits heal and permanently increase your max mana.
Comet on Zyra allows you to pump out massive amounts of damage with repeated Comet procs thanks to your plant attacks reducing the cooldown with every hit they land.
This rune page is heavily focused on lane harass and pressure, and to do that you're looking to spam your spells quite a bit. Manaflow empowers you to do more damage with Aery and Scorch.
If you think you can manage your mana well enough, Ultimate Hat is a solid alternative.
Because Zyra doesn't traditionally build CDR items (Rylais/Liandries) the extra bit of free CDR means more DPS you can pump out in teamfights.
Again this rune page is heavily focused on lane harass and Scorch is good at that, often out-damaging most Keystones early. Constant plants attack with proc this very effectively.
Magical Footwear on Zyra means you get to buy that crucial first damage items just a bit quicker than usual, making your mid-game teamfights extremely powerful.
Biscuit Delivery provides you with the sustain necessary for taking aggressive lane trades while also buffing up your mana pool a bit so you can opt into damage items rather than mana.