Convertibility refers to whether or not a currency can be directly exchanged for either another currency (e.g., a complementary currency for a national currency, or one national currency for another) or a commodity (e.g., gold).
Whether or not complementary currencies incorporate this feature depends on what they want to achieve. For example, the Brixton Pound is convertible into Pound Sterling. This helps to build trust, as users know that they can always “get their (convention) money back” if unable to spend the Brixton Pound. In contrast, the WIR Bank does not allow convertibility. This has the advantage of ensuring that wealth stays within the network and continues to circulate between members.