TL;DR: A share code is a 9-character code from the UK Home Office used to prove your right to rent in the UK. You can retrieve a code starting with "R" at GOV.UK.
A share code is a unique 9-character alphanumeric code issued by the UK Home Office to digitally prove immigration status, right to work, or right to rent. This is used in the Thirdfort app to verify you have the right to rent in the UK.
You can find your share code here: https://www.gov.uk/prove-right-to-rent/using-other-documents. It will begin with the letter R.