What is the function of sodium dodecyl sulphate in a DNA extraction?

The principle role in DNA isolation that sodium docdecyl sulphate (or SDS for short) provides is in the break down of the cell wall/membrane of a bacterial cell.

The long hydrocarbon chain on the end of SDS is extremely hydrophobic, while its sulphate head is very hydrophilic. Because of this SDS will tend to stick itself into the cell membrane (because the inner part of the membrane is hydrophobic, and the outside is hydrophilic). However, SDS does not exactly fit into the membrane well, and will disrupt it, eventually causing the membrane to collapse.

Additionally, SDS's hydrophobic tails will tend to surround integral membrane proteins in the membranes of the cells (because the proteins are largely hydrophobic as well), and because of this surround of hydrophilic SDS heads, the protein will forceably be removed from the cell membrane. Once again, this contributes to the breakdown of the cell membrane.