You can evolve your card by clicking on team -> the card you want evolve -> evolve
When you evolve a card 5 times its becomes a higher tier. This means if you evolve a 5* Card five times it will be upgraded to a 6* card.
Why I should evolve? Edit
When you evolve a card, it will open up "Awakings" which will make the card stronger. Also the card gains more life, attack, defense and magic per level. Many cards have simple awakings such like "10 % more life" or "20 % more defense", but there also cards with special awakings like Natsu, Erza, ... when you evolve Natsu 5* for the first time - the crit chance will increase by 40 % when Natsu´s life is under 50 %.
When should I do it? Edit
You can evolve from the beginning. But you should use "advance" 9 times before. Because when you raise up to the next tier (from 5 -> 6 Star) it will halve the advance counts. This means you can use advance 5 times more - this will give a huge boost for you card. The best ist to evolve 4 times and than finish until the card is advanced 9 times