In the scenario I mentioned, it just means that any rights the adult occupier has are postponed behind the rights of the Lender.
The classic example is -A buys a house with a Mortgage. A's partner (B) is also going to be residing in the property, but is not on the Mortgage. B signs the standard Occupier's Letter provided by the Lender.
A fails to pay the Mortgage and the Lender re-possesses.
While living there, B had previously paid for and built a Conservatory at a cost of £30,000. B therefore has what is called an "equitable interest" in the property.
Property is repossessed and sold for £120,000. The amount outstanding under the Mortgage was £110,000. The Lender is entitled to their £110,000 back, and B is not entitled to try and re-claim his full £30,000.
However, from the equity left over and which is paid to A (£10,000), B would the make a claim against A on the basis of his equitable interest.