Character cards and their equipment can be made stronger by upgrading them. There are a few ways to do this. Upgrading/Strengthen, Ascending order, and Evolution are the most common ways.
In order to upgrade your cards, you can sacrifice other, easily attained character cards and equipment to make them stronger. However, the level of the character and its equipment can only be increased up to your level on your account. In order to increase your account level, you can do tasks to accumulate Exp points, which will in turn raise your account level.
To strengthen your team further, you can use Ascending Order on your character cards, increasing their power at the cost of gold coins. However, in order to ascend beyond 3r(R: being the method used by the game to see what level your cards are currently ascended to), cards of the same star rating must also be sacrificed. The max level you can ascend your character cards to is 9r. Cards can also be evolved, which boosts their base stats and unlocks additional "awakenings", at the cost of evolutionary crystals and a copy of the card that is being evolved. These awakening bestow extra abilities upon the character, and can often turn the tide of battle.
*Note: it is highly recommended that before performing the final evolution of a 5 star card, you complete the ascending process up to 9r in order to maximize stat gains upon evolution to 6 star card. Once becoming a 6 star card, the ascending level is halved, allowing you to perform ascending order once again.
Training water can be utilized to slightly increase the stats of a character card. Each character card has a certain number of "Potential Points" which is the amount of times that character can use training water. It can take a while to fully train all the members of your team, but once you have finished, you will obtain an edge over other players who haven't fully maximized the potential of their team.
Your team can also be strengthened by refining their equipment, which costs refining stones and gold coins to raise the equipment's base stats.
Finally, if you have a character that you've put a lot of work into, but no longer have a use for, you have the option to use Apart on them. For the cost of 50 diamonds, you will be able to sacrifice that card and get back the Evo stones, Experience points (in the form of EXP. Crystals), and other benefits that you've put into the card in order to be used on another character.