In CentOS 7 MySQL has been officially deprecated and the database of choice is MariaDB
MariaDB is a fork of MySQL created by the lead developers of MySQL when Oracle acquired Sun.
A detailed history about MariaDB can be found here
As far as feature comparison there is a good article on MariaDB show casing the technical differences.
First, add the community MySQL repo to CentOS:
rpm -Uvh http://dev.mysql.com/get/mysql-community-release-el7-5.noarch.rpm
Second, install MySQL:
yum install -y mysql-server
Finally, enable start on boot
chkconfig mysqld on