In terms of regulating itself, how is a selectively permeable membrane important to the function of the cell?
A selectively permeable membrane allows certain molecules to pass through, but not others. Having such a membrane allows a cell to maintain control over itself both by preventing important cell contents from leaking away, and by only letting specific substances enter the cell from the outside.
Some substances cross the cell membrane by passive processes, which means that the cell does not have to expend energy to move those substances. This is important for substances like water, which moves through the passive process of osmosis; many cells are moving water constantly, and if they had to expend energy to do so they would have little left to do anything else.
Other substances, such as glucose, are moved by active processes which do take up energy; however glucose is an important molecule that the organism has to make an effort (through either photosynthesis or feeding) to obtain. Consequently it is necessary for a cell to be able to control the entry and exit of glucose, lest it leak out and be lost.
In sum, the selective permeability of the cell membrane makes it much easier for the cell to maintain homeostasis, the chemical stability necessary to life.