A stream channel is stable when the forces acting on it balance out.
In our model a carpenter's level pivots as it reacts to the forces acting on it. When the forces in each direction are equal, it is horizontal (in equilibrium).
The stream channel is where the work of the river, i.e. the transport of water and sediments, occurs. As you view the river it is the portion of the river between the "bankfull" marks on each side of the river. This is the most active portion of the river and this is where changes will first be evidenced.
Water and sediments enter a segment of the stream channel on the upper end and leave on the lower end. Unless water is somehow added or withdrawn within a segment, the water gain at the upper end of the segment is assumed to be approximately balanced by the water loss at the lower end.
As the water moves through the segment it loses elevation. It is the loss of elevation and the accompanying change of the water's potential energy to kinetic energy that gives the stream the ability to do the work of moving sediments through the segment.
If the water has just enough energy to move the same quantity of sediment out the bottom end of the segment as entered the upper end, the stream is said to be in balance or in equilibrium. (The stream does not need to move the same sediment out the bottom as entered the top, it only has to move an equivalent amount of sediment.) Because the losses equal the gains this type of equilibrium is called a "dynamic equilibrium". The stream channel is not static - the sediment particles do not remain in place. Instead it remains the same as it constantly changes because the losses equal the gains.
If the water in the stream has energy to move more sediment out of the stream segment than entered from above, the additional sediment lost will be seen as erosion. On the other hand, if the water in the stream does not have enough energy to move all of the sediments that came into the upper end of the stream segment, the gain of sediments will be seen as deposition.