A profile visit only includes the visiting member's name and the date it was left. There is no way for someone to attach a message to their visit to your profile. Private messages are sent directly to another member and include the ability to write a comment or share a warm memory.
To leave a message for someone, you can post it as a note on their profile or send a private message.
To check for any private messages you've received, visit your Classmates Inbox, then select My Profile and Private Messages.