In the beginning, you owe more interest, because your loan balance is still high. So most of your monthly payment goes to pay the interest, and a little bit goes to paying off the principal. Over time, as you pay down the principal, you owe less interest each month, because your loan balance is lower. So, more of your monthly payment goes to paying down the principal. Near the end of the loan, you owe much less interest, and most of your payment goes to pay off the last of the principal. This process is known as amortization.
The programs vary in what they can offer. In some cases direct financial assistance may be provided to help you pay your mortgage for a short period of time. Payment plans or reduced monthly payments may be offered. However most of the government programs and non-profit organizations will help facilitate some form of loan modification to qualified homeowners. This will provide families time to get back on track by ideally lowering their monthly payment, reducing interest rates or waiving fees.