It’s been said over and over in my biochemistry books that the cis-double bonds between the Cs in the hydrocarbon tails in triglycerides causes a kink. This kink disappears when the bond is isomerized into its trans conformation. What is it about the cis bond that causes the kink?
The best way to demonstrate this kink is with pictures. Usually we have some motivation to try to represent the molecule on a single line. So for oleic acid (cis-octadec-9-en-1-oic acid), we often get pictures like the following:
Elaidic acid, the trans-isomer is also sometimes depicted unhelpfully to save space:
The second structure for elaidic acid is not as misleading as the corresponding structure for oleic acid. A better bond-line structure for oleic acid is:
Better yet, here are some space-filling structures from Wikipedia based on crystal structures of both molecules.
And here's $\gamma$-linolenic acid, which has three cis alkenes in it: