In layman terms, home equity refers to the actual stake a borrower has in the property after accounting for debt obligations against it.
For example, if a house was valued and purchased at $500,000, with an 80% loan to value from a lender, the new owner would have a $100,000 equity stake in the house made up of the down payment at the point of purchase.
5 years later, after paying down $100,000 of the loan principal, the outstanding mortgage would be left with $300,000, and his equity in the house is raised to $200,000.
However if the property value has appreciated by $40,000, his equity stake will become $240,000.
Another 5 years later, after repaying an additional $100,000 towards the home loan, his home equity increases to $340,000.
Should the property appreciate in value by another $50,000, his equity stake becomes $390,000 on the house now with a market value of $590,000.
The first and second mortgage on the house will now total $280,000, and home equity plunges to $300,000.
Whether he used that $90,000 to make the down payment for a rental property or uses it to travel the world twice over is none of our business.
What matters is that the extended example above should give you a good general idea of how the dynamics of home equity works.