Evolve is the process of using two of the same cards together to create a more powerful version of the card. If you only have one card you can use Tsukuyomi instead. Maxing cards is recommended since the stats will carry over.
R cards have four evolution stages, R, R+, R++, and HR. SR cards have three evolution stages, SR, SR+, and HSR. UR cards have two evolution stages, UR and HUR. I recommend using 8 R cards, 4 SR cards and 2 UR cards, all MAXED to do perfect evolution.