Participants are the outside or external people that are invited to plans. There are 2 types of participant:
Owner participants are added and invited immediately when a plan is created. A plan must always have an owner participant.
First open the plan you want to add a participant to. Then click the Person button at the top right of the page:

You'll see the people page, which is where you can manage the people (participants and users) invited into the plan:
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The participants are shown in the top section, with the users below. Click Invite someone to invite a new participant.
You'll then be able to type an email address for the new participant and type a message to be included on the invite email:

Finally click Send invite to complete.
Tip: Once they've been invited, but before they accept the invite, you can use the Resend invite button to invite again.
In the same place, you can Remove any invited participant from the plan. The owner participant and any user with full access to the plan can do this.
Note: Invited participants can see this page but can't invite other participants or remove them.