Cellular hypoxia leads to reduced ATP, resulting in Na/K ATPase down regulation reducing the activity of the Na/K pump.
(edit removed the original link since I'm limited to two links in a question currently and the newly added link is more relevant)
Resulting in increased cellular Na, which attract water into the cell which would lead to cellular hypertrophy.
Without sufficient supplies of ATP the plasma membrane of the cell can no longer maintain normal ionic gradients across the cell membranes and the sodium potassium pump can no longer function. This changes the ionic concentration of potassium and sodium. Potassium leaks into the extracellular space and sodium followed by water will move into the cell, causing cellular oedema and an increased intracellular osmotic pressure (Edwards, 2001). The cell may eventually burst.
The high intracellular potassium and low intracellular sodium and calcium concentration are maintained by active transport systems. Thus, one of the most rapid effects of hypoxia, and a shortage of ATP, is perturbation of the normal ionic gradients across the cell membrane, with a rapid efflux of potassium from the cell, and movement of sodium and calcium into the cell (Gosling, 1999).
Increased sodium in the interior of cells result in water also entering the cell, driven by osmotic forces causing cellular swelling and distortion, which may interfere with organelle function (Buckman et al, 1992).
I've always heard other explanations for the 'pump' after workout, with the most frequent explanation being along the lines of
during intense muscular contraction, this force inward momentarily occludes the vasculature, backing up blood flow through that particular muscle group. A compensatory increase of blood pressure forces plasma from the congested capillaries into the interstitial spaces of the muscle cells.
However, the above seems like it should be a significant factor that I've never heard mentioned in sports physiology texts and papers. I can't find information on the time course for reversing cellular oedema - ie would it be maintained long enough after exercise to account for the 'pump'.