How can I share a board outside my organization but prevent that person from sharing?

@AliceMeade123 - If the person you are sharing with only need to View or Comment, and the board resides in a Starter or Education Plan, you can add them as a Guest Viewer or Commenter.

If they need to Edit the board, and you have the Consultant/Business or Enterprise Plan, you can add them as  Guest Editor - Note: your plan admin may need to enable the Guest feature More on this here:

https://help.miro.com/hc/en-us/articles/360021415119-Collaboration-with-guests

Another option is the Visitors feature, but the recipient of the board link could easily share it with anyone on the Internet.

I need to make sure that the person I am sharing with does not forward the board to other people

Do you mean forwarding a link to the board or a copy of the board? If a copy, you can adjust the a board’s permissions to disallow anyone from outside of the team from copying content from the board, exporting content, or duplicating the board. More on this here:

https://help.miro.com/hc/en-us/articles/360018350399-How-to-allow-or-restrict-copying-and-exporting-boards-and-content