When you are verified, the community knows that you are who you say you are - you will receive a badge to reflect this. When you join Plus, you gain the option to request verification of your account. This can be removed if you'd like, but we think it's looks cool.
Once you purchase a Plus membership, you will see a link to become verified. The link will prompt you to submit two or more social media links that include your Minds profile. From there, the Minds team will review the submission and verify that you are who you claim to be.
Learn more about Minds+ here