It is one way for a company to minimize negative investor interpretation of its corporate actions.
If an already public company chooses to issue stock, the market usually interprets this as a sign that the company's share price is somewhat overvalued. To avoid this negative impression, the company may choose to issue convertible bonds, which bondholders will likely convert to equity anyway should the company continue to do well.

There are a number of reasons why the investors and/or the company would prefer going for convertible debt.
For the company, the reasons are clearer. If the company believes its equity will be worth more at a later date, then it will dilute less by issuing debt and converting it later. Also the transaction costs, mostly legal fees, are usually less when issuing debt vs equity.
For investors, debt is senior to equity in a liquidation so there is some additional security in taking a debt position in a company vs an equity position.