So no, it does not mean that God physically intervenes, in say, the orbits of the planets – contra Newton, who asserted that God did in fact intervene to keep the planetary orbits consistent. In fact, his entire program of physics was theological, with time and space being the divine sensorium, or how God was presented to the world/universe/whatever. Newton’s formulation of laws are very theological, in fact, and represent a radical departure from the Aristotlean conception of ‘laws of nature’ which was more concerned with immanent teleology.
Now, with regard to intervention of the divine kind, the classical picture holds to what is usually called primary causality:
‘Providence works at the level of what Aquinas would call primary causality: that is, it is so transcendent of the operation of secondary causes- which is to say, finite and contingent causes immanent to the real of created things…’ (David Bentley Hart, ‘The Doors of the Sea’)
Hence, the natural order of things doesn’t simply run off its own steam, a la deism. The primary cause of things is the source of the secondary causes (secondary causes being what we normally think of causes, gravity, human agency, etc) but also transcendent of it. The difference between this and deism is pretty big. God as the sustaining cause of all that is, then, refers to both his upholding of all existence as well as the grounding of all secondary causes in him.