Debt Consolidation is basically taking multiple debts or bills and joining them into one.
If for example you owe five different bills that have to be paid monthly on five different dates, one can 'consolidate' or 'bring together' these debt to one single date and debt, and so pay only once a month as opposed to five times.
This can be done for example by taking out a sixth loan (with a bank, lending firm or P2P Lender) in the full amount of the five debts, fully paying off the five debts and then only paying the one remaining sixth debt.
This can have conveniences as well as inconveniences.
Depending on the amount one owes and the interest rate one pays, this might make a big difference as it could lower the rate and thus the monthly amount one has to pay.
If however the interest rate on the sixth loan is higher than the rate one pays for the original five bills, then one may end up paying more in monthly fees than one did before.
Debt consolidation -- taking out a new loan to pay off previous ones -- is a very delicate matter and one needs to be careful, because it actually doesn't get you out of debt but actually gets you deeper into debt. But it does give you the opportunity to deal with your current debts by easing the weight on your shoulders.
To illustrate this, imagine you're sitting in a small sinking boat. Plugging the holes in that boat won't get you to shore, but plugging those holes does give you the chance to get back to shore.
Thus, consolidating all of your high interest loans into one well thought out debt consolidation loan at a very good rate could save you tons on the amount of interest you're charged on your monthly debts.
So then when the new bill comes up you might pay less now than you did before.
And that can be a really good thing.