Phenomenalism is best thought of as a secular idealism. Like idealism, it holds (roughly) that objects are dependent upon our perceptions of them. Unlike idealism, however, it is not committed to the existence of a God who is constantly perceiving everything.
Idealism holds that objects exist only insofar as they are perceived. It therefore faces the dual problem of explaining what happens to objects when we cease to perceive them, and why different people’s experiences are consistent. To solve both of these problems, idealism invokes God.
Phenomenalism differs from idealism in that it holds that objects exist insofar either as they are perceived or as it is possible to perceive them. Phenomenalism is thus a weaker theory than idealism. Whereas idealists are committed to the idea that an object that is not perceived does not exist, phenomalists can allow that such objects exist insofar as it is possible to perceive them. They therefore have no need to invoke God to explain objects disappearing and reappearing when people cease and recommence perceiving them, as the idealist does.