Summon
Playing through the Dragalia Lost's campaign on itself is already interesting enough, but beyond reasonable doubt, a lot of players are all about its summon system -- gunning for those most sought after, rare playable Adventurers. Additionally, the same system introduces Dragons (can be equipped to you Characters and be summoned while playing), and Wyrmprints (accessory like items).
Adventurers are the playable Characters that you get to control when performing Endeavors (in-game Missions). When you summon a new adventurer, you'll be pitched with an over-arching lore that will introduce the character to your crew and your on-going adventure.
These Adventurers also have varied rarities that are graded from 3 stars, 4 stars and 5 stars (the more stars it has, the rarer and stronger it is). Apart from this, they also vary in their elemental affinities - which is like an additional RPS mechanic of the game. The element variation includes; Fire, Wind, Water, Light, and Shadow Elements. Lastly, each adventurer has its unique set of active and Passive Skills that you gradually get to improve as you put work on their Mana Circle.
Besides the Adventurers, you can also randomly draw out Dragons from summon. These units are playable as well as you equip them your adventurers. Similar to how you are introduced in summoning one while in battle, you can generally assign one for each member in your party. Apart from providing the summon capability when the concluding gauge fills-up, each dragon equipped in the party also adds up its passive bonus/es to the party.
Similar to Adventurers too, Dragons have element variations and will provide a bonus stat/s when it gets equipped to a character that shares the same elemental affinity. Dragons are graded with star-ratings to similar to that of Adventurers. If by any chance you're having difficulty drawing 4-5 star ones in the summon, know that by simply playing through the campaign, you'll earn much of the 4-star Dragons.
Wyrmprints are accessory/card like items that your Adventurers can equip in the game. They provide you with Passive Skills or stat bonuses that are essential in improving your overall might. They are also the most common drops when performing a summon. They are also graded depending on their rarity, and higher rarity means it pretty much endows you a great passive buff. Wyrmprints are upgraded similar to that of adventurers, and Dragons -- where each level of upgrade gradually increases the stat bonuses it provides.
Summoning Options
Although there are 3 options for you to summon, the one that would probably stick out to you is the "Tenfold Summon" option. It is not cheaper than the Single Summon (which does the same thing but draws out 1 items per summon), but it guarantees one 4-5 star summon every time you use it. The other option called "Daily Deal" is primarily a discounted offer which requires micro-transaction. During the first week of the game, it also gave away free summon vouchers which can be used to summon - free of charge.