You can visit the persons profile to see the full Intro they sent you. Like them to move them to the Conversations page, or Pass on them to see the next Intro.

What happens when you send intro on OkCupid?

Once you send an introductory message to someone, we wont show them to you again on OkCupid until they like you back. If they like you, theyll let you know by liking you back or replying to your message.