(Credit for the video above: SanchoPanda VTW)
You cannot just put a bunch of monster cards on your team and expect to clear everything in the game. You will fail. That team will be absolutely awful!
In the video above (though somewhat outdated), this is just a very basic example of team synergy. There are more teams that are better in terms of synergy and working with one another. It is fair however, to point out that some of the best teams with excellent synergy can only be obtained from the gacha.
In the photo above, that is one of my best teams (the sixth card is a friend helper and not one of my cards). The basic idea of this team is to match as many different color combos as possible. The more combos you make, the more damage you'll do. The Leader Skill of the first monster triggers that effect -- a Leader Skill is on the very first monster in your team; it's the only Skill that is always active.
The active Leader Skill of my monster card converts all orbs on the current board into other element orbs. Very useful when you don't have enough to make a combo.
The second monster's active skill reduces damage by 75% for two turns.
The third card reduces enemy HP by 20%, and clears binds. When a monster is bound, it's unusable for a set number of turns. Think of it not being there at all.
The fourth monster multiplies the attack of all God type and Dragon type monsters on the current team by two (all of them are at least one of those types).
The fifth one reduces damage by 50% for three turns.
The sixth card (the friend helper), is exactly the same as the first card (including the Leader Skill).
In more simple terms, I can take less damage, reduce enemies HP, multiply my own attack, and deal colossal damage by matching all orb colors -- as you can see, all of my cards cover at least one of every orb element, except for heart orbs. Heart orbs simply heal you when you match three or more.