A phospholipid has a charged, hydrophilic phosphate head and a neutral, hydrocarbon hydrophobic tail. In a phospholipid bilayer, two phospholipids combine tail-to-tail such that the two outer, or exposed, surfaces are comprised of the polar phosphate heads. The bilayer can function as a cell membrane; it can keep what is in "in" and what is out "out". It can also regulate critical cell functions such as pH and ion balance through the incorporation of proteins in the bilayer that can serve as ion pumps. Clearly, any disruption to the bilayer could allow the cell contents to leak out and bad stuff to leak in, which would lead to either cell inactivation or cell death.
The mechanism of action of quaternary salts on lipid bilayers is still an active area of investigation, but here is a simplified overview of what is thought to be happening. . The first step is thought to involve the electrostatic interaction of the positively charged ammonium ion with the exposed, negatively charged bilayer surface, followed by incorporation of the hydrocarbon chain of the ammonium ion into the bilayer. The electrostatic interaction affects membrane surface pressure which, in turn, disrupts cell function. Shorter chain lengths (n=12-14) are more effective against gram-positive bacteria, while longer chain lengths (n=14-16) are more effective against gram-negative bacteria.
Here's a reference to a recent thesis (2012) that studies the resistance of bacteria to quaternary ammonium compounds. Section 1.2 (pages 2-5) provides a clear, concise summary of the latest thinking on the subject.