Why do double bonds cause kinks in fatty acid chains?
Instead of zig-zag, zig-zag, zig-zag etc. it now goes zig-zag, zig, zig-zag, zig- etc (the bold zig is due to the cis double bond). So the direction of the alkyl chain on one side of the cis double bond is different from that of the alkyl chain on the other. You could partially correct for that "wrong turn" by rotating a single bond by $180^\circ$, but that changes a staggered conformation into an eclipsed one.

Here is a link to a 3D model: http://www.biotopics.co.uk/jsmol/fattyacids.html and a snapshot in case the link goes away: