Karma is volitional action caused by intention (cetana). The result of karma is its fruit (karmaphala). Karma are of two types – wholesome (kusala) and unwholesome (akusala). Both of these lead to rebirth (samsara). Wholesome karma leads to a superior rebirth while unwholesome karma leads to an inferior rebirth.
Rebirth does not necessarily pertain to the rebirth of a lifespan. Every moment is a rebirth so long as it is conditioned by an action from an intention. Rebirth is akin to sustainment or continuity. Actions not stemming from an intention are without karma and therefore without fruit. Karma without fruit is therefore desirable in Buddhism.