Alright, this isn't really Laravel specific, but let's think about it...

Basics

We'll most definitely need two tables, which we can call users and invited_users .

For our users table, you simply put whatever details you need, such as first name, last name, email, password, etc.
For our users_invited*, the bare minimum is an inviteCode and used [bool] column, but a referrer column is useful if you want to give something to the referrer.

*I chose this name because both users and users_invited will appear near each other in the database when managing your db

Implementing the invite system

The best way to do this as I see it (there are of course different options) would be the following:

when a user sends an invitation to a certain email, we create a hash of this email and makes this the unique inviteCode mentioned. This will then be appended to the link that is sent to the referred person. e.g http://example.com/?invite=6c132a79dbbc044c44952db50ed9e3b7. We then add the following data to our users_invited: inviteCode, referrer (optional, but needed for an award system), email (also optional, but convenient to auto-fill registration field). Other than that, you can of course add whatever information you wish to generate date for users. E.g, you might wanna check how many invites a user has sent and how many of these were accepted to see the success rate, or store which people a certain user has invited (although this is easily done if you have both a referrer and email field in the users_invited table.

Recap

We have two tables: users and users_invited.
The process will follow the following structure (excluding front-end part like response to referrer):

1. User enters an email address to send the invite to
2. We hash this email. We can use a simple hash like MD5 to decrease load if we want to, since we're not storing anything super sensitive (even though you really should have a good reason to use MD5 over a more secure hash when secure hashing is built into Laravel and hence easier to implement)
3. Create an entry in our users_invited table containing the inviteCode and referrer email address.
4. Send an email to the invitee containing a link that somehow incorporates the inviteCode.

If our referral clicks the link we want to do the following:

1. Check that the code is valid and unused (if we want to have single-user invites)
2. Present our invitee with a registration form if step 1 succeeds
3. On submit, change the used column of the invited_users row affected to 1 to ensure the code cannot be reused.
4. If you want to, notify the referrer that the invitee has accepted the invitation (if we stored the referrer's email).

Some things to consider

The method presented is made for a system based on exclusive invites. E.g something that requires an invite to join. If you instead only wish to have a referrer/referral system where a referrer gets granted some perks by making more people join, I'd suggest you skip the entire users_invited table and simply store the hash of a person when they register. Then use this hash in any invitation url generated. This means that the url will be the same for every invite sent by person x.

I think that was it. If you have any questions, just ask!

Cheers!