Good morning Valerie,
We can't have you starting WW3 over this.

I'm not a mortgage lender but I am an accountant. Please talk with a few lenders before making any decisions and get some hard numbers. Always. (LOL, I'm so bossy!)
Equity is basically the piece of something that you personally own. Think on that for a second - I probably didn't phrase it well.
The most basic accounting formula which rules our profession is Assets equals Liabilities plus Equity. Let's say that your house is valued at $100,000 (asset) and you currently owe $80,000 on the mortgage (liability). That means your equity is $20,000 only in the strictest accounting sense.
This basic formula does NOT consider the fact that things either appreciate or depreciate.
Homes usually appreciate or increase in value. Housing prices go up, perhaps home improvements have added value to your home, perhaps the neighborhood is in the process of "upscaling" itself, etc. These kinds of events would increase the asset portion of the formula - and consequently this would increase the equity portion as well. Make sense?
If your home was originally valued at $100,000 but today is valued at $125,000, then your equity jumps from the $20,000 to $45,000.
Home equity is basically the fair market value less any claims (mortgages) against it.
Since the value normally increases over time and the claims against it decreases over time, property investments are one of the wisest decisions you can make.
You should consider any home equity loan to be a second mortgage. It is a claim on your poroerty, and defaulting on the loan allows the lender to take possession of your property. However, it can also be a wise investment if you have substantial untapped equity and you plan to either 1) dramatically increase the value of the property through an addition or other improvement or 2) pay off high interest debt.
Let me know if you'd like examples to demonstrate that. It's easy enough to do - just remember that the A = L + E formula can apply to a portion of your finances and to all of your finances. People should always have a pretty clear idea of their net worth at all times...simply the market value of what they own less everything they owe to others equals their equity (or profit).
On appreciation versus depreciation ~ some things increase in value over time but other things decrease. Cars are an excellent example of a depreciable asset. The moment you drive a car off the lot, it decreases in value. If you bought a new car for $18,000 and then tried to sell it immediately, you will not get the $18,000 for it. It is already worth less than what you paid for it.
The only reason I mention that is because so many people trade in their cars while they still owe money on it. They are basically refinancing their original loan - which increases the price of the new car they just bought. Makes no sense whatsoever.
Anyway, I hope this helps somewhat. Please let me know if you would like me to clarify anything. Hopefully, someone with mortgage lending experience will be able to round out my reply. Be cautious and wise - you work too damn hard to take these things lightly.

We are what we repeatedly do. Excellence, then, is not an act but a habit.
Aristotle