On A Grace Period - This typically means the membership has been canceled and they are on a grace period until the end of the billing cycle. They are still able to sign up and take classes or view video/media content until the membership has ended.
On Trial - If you have created a Membership will a Trial Period, this means they can sign up for classes/sessions and would not be charged until the trial is over. They have free access to the sessions assigned in the membership. Their billing cycle will start at the end of the trial. (Below is an example of a membership with 7 day trial).
Active - This means your client has an active ongoing membership-you can see how long they been a member (Sign up date), and their current billing cycle and when their next invoice is depending what their recurring billing cycle (weekly, monthly, annually).