These are the in-game currencies! You can see your totals located in the upper left corner of your screen. Melodia is the musical note icon, and the Gemberries look like a berry. These are acquired during normal gameplay but if you want to speed up your progress you can purchase these from the shop.
Melodia
Melodia is primarily obtained from harvesting your birds when they are ready but can also be a possible reward or gift in other places too! The amount of Melodia harvested from each bird will vary with the size, rarity and level of each bird! The more common birds will harvest quicker but with smaller Melodia amounts, and rarer birds will take longer to harvest, but yield a lot more! You will also get a certain amount of Melodia for a bird if you sell them. Melodia is used to expand your Forest, set Food Flower shifts and can be used to purchase some Daily Deals too.
Gemberries
Gemberries are earned around the forest as some Mission and Achievement rewards, for catching a floating petal, as a possible reward from the Video Bat etc. and are generally used to hurry things! You can hurry Food Flowers, incubating eggs, fledglings, missions, event timers etc. They are also used to upgrade Food Flowers so they yield more Gnats and to buy items like Feathers, Lesser and Greater Spirits and Event Seeds and Mulch to speed up your Event progress.