There are several possible reasons why you might get an error message when you try to join a group from an email invitation.
You're clicking an invalid invite
The group might have been deleted from Google Groups. Nobody can join a deleted group.
Or, the invitation could have expired. Group invitations expire 7 days after they are sent. If your invitation expires, you can ask the group owner or manager to send you another invitation.
You got uninvited or banned
If you're banned from a group, you'll get an error message when you try to join it. A group owner or manager can also cancel your invite. In both cases, contact the group owner or manager and ask them to unban you or invite you again.
You're using the wrong account
Group invitations are sent to a specific email address. If you try to accept the invitation using any other email address, including an alias or another account that you own, you'll get an error message. Check the email invite and make sure you're signed in to the correct account before you accept the invitation.
You're already in the maximum amount of groups
You can only be a direct member of 2,000 groups. If you're already in that many groups, you can't accept any new invitations. Leave one of your groups and try accepting the invitation again. For more information about membership, go to Understand Groups policies and limits.