There are two major types of municipal bonds you should be aware of: general obligation and revenue.
General Obligation bonds are backed by the "full faith and credit" of the issuer (just like most other bonds). The key word is credit. The concept is very similar to your credit card. The banks don't really know if you're going to be able to repay...you got the card based on full faith and credit.
Revenue bonds are sold against the future revenue that a project will generate. If your project will bring in a revenue of $20,000 next year, you could sell a revenue bond for $10,000 and get some immediate funding. The bondholder would then have a claim on some of your future revenue.
Because of their unique tax status, the interest that you earn on a munis are almost always exempt from federal income taxes. If you live in the state that issues the bond, you're also exempt from state taxes!
And if you live in a city that issues the bond, you're exempt from city, state, and federal taxes! Not too shabby.
For revenue-based munis, the type of project being financed can also affect your taxes. Interest from bonds sold for "public good" projects or "qualified private activities" are usually free from federal taxes. Interest from munis issued for regular private sector projects are most likely NOT tax exempt.
Notice I said ALMOST always tax exempt. Certain restrictions do apply, and some munis are subject to the alternative minimum tax. Make sure you check all the facts before buying any investment.
When you're comparison shopping, keep in mind that comparing the coupon rates of muni's (and other taxable bonds for that matter) can be misleading.
Taxes will end up reducing the net income on taxable bonds. This means that a tax-exempt municipal bond has a higher after-tax yield than a corporate bond with the same coupon rate.
Muni's typically have a longer time to maturity that other types of bonds. On the upside, interest rates are typically higher than CDs, Money Market Accounts, etc. On the downside, these bonds are harder to buy and sell (i.e. they're less liquid).
Normally, the probability of a local government body defaulting (being unable to pay off loans = bankruptcy) is very low. "Very low" does not mean that it cannot or will not happen; there are many state and local institutions that struggle to maintain a balanced budget.
When a local governments balance sheet is bad enough to catch the eye of a bond rating agency, a municipal bond's rating might be lowered.
If that happens, the local agency may have to raise rates in order to attract investors. Or, they could lower the price and keep the rate the same.
Municipal bonds typically require a minimum investment of at least $5,000. If you're worried about the price tag, check out "mini-munis". They are designed for bond investors with smaller budgets.