A monoline insurer, in the context of financial markets, guarantees the repayment of bonds. In other contexts the term may merely mean a specialist insurer. The word “monoline” by itself may also simply mean a company with a narrow range of business. In the financial sector and “monoline” is almost always synonymous with “monoline insurer” or “monoline insurance”.
Like any insurance, monoline insurance is a transfer of risk. The default risk is transferred from bold holders to the insurer. Bondholders are left only with the residual risk that the monoline insurer will also default.
The effects of the insurance (really more in the nature of a guarantee) is that the risk premium on the bond shrink, reducing the return investors require (or get). However, the issuer has to pay a price for this, as the insurer must be paid.
In a perfectly efficient market there would be no reason to use monoline insurance, as the cost of insuring the bonds would have a value equal to the savings from the lower risk premium. There are many reasons why such guarantees are viable in the real world: differences in access to information and in demand for credit risk are obvious explanations.
The existence of monoline insurance also makes bond issues easy to market, as the credit risk is essentially that of the (high credit rating) insurer, simplifying analysis for most investors — analyse one monoline insurer and you have analysed the default risk of all the bonds they insured.