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Debt consolidation loans are , generally, secured against the equity in your home through refinancing.  When you refinance, you are usually changing the terms of the mortgage on your home to include most, or all, of your equity.  This is often done through a debt consolidation.

In debt consolidation, the amount of your monthly payments are added together.  This would include things like car payments, credit card debt, and student loans.  This sum is tallied against the amount of equity that you have in your home. 
If you have enough equity in your home to pay down these debts, you will be offered a refinancing of your mortgage to consolidate your debt.  If you have more than enough equity in your home to pay off your monthly debt, you may be offered cash on top of the debt consolidation.

The terms of your mortgage are renegotiated regarding interest and length of payment.  For instance, you might be offered a lower interest rate against the total sum, and your term may be extended from ten remaining years to fifteen or even twenty. 
Because of renegotiated terms and interest rates, it is very important to carefully consider the details of your debt consolidation loan.  This money will be secured by your home and if you wind up unable to repay it, your home could be at risk.

Certainly, do not take the first debt consolidation loan offered to you.  It is often wise to first approach the bank or lending institution that currently holds the mortgage on your home, since you already have a relationship developed between you. 
Also consider local banks or lending institutions in your community, as well as online resources. 
There are many lenders specializing in debt consolidation, so be sure to take your time and shop for the best deal, like you would for anything else.