Oxygen is important for yeast to be able to develop their cell wall properly. A weak cell wall means a few things. First, cell wall permeability is increased. This isn't a huge issue in a beer around 1.040-1.050. Any higher and the sugary water can possibly suck all the water out of the cell.
The second is that a yeast cell cannot properly bud. Yeast reproduce by budding. If the cell wall is thin and brittle, it cannot reproduce well.