These are called Lesser Spirits, you can also get Greater Spirits too!
Lesser Spirits are the little floating blue orbs that will appear in the forest every now and then when you collect Melodia from your birds! Greater Spirits look similar but have little wings and do not spawn in the forest, these are found in other places.
Tap to collect Lesser Spirits in the forest, and they will go to the little shrine area located by the Enchanter Fox. You can then tap and drag these to the Enchanter Fox to help him Enchant Feathers, which you can then use on the Summoning Tree to Summon specific birds.
You can purchase Lesser or Greater Spirits using Gemberries when tapping the Enchanter Fox.
Greater Spirits will give better Feathers than Lesser Spirits. Sometimes you can buy Spirits from the shop Daily Deals, or you can earn these as rewards from Achievements, Missions or they may even appear in gifts from friends!