Lipid packing defect
It would help if you could delimit in which cellular of molecular context you would like to understand packing defect, for exemple during vesicular budding or lipid droplet biogenesis.

In the larger context of cellular membranes lipid packing defect occurs when there are transient "holes" made in the phophosolipid bilayer.

These packing defects can be caused by the chemical nature of the phospholipids present in the membrane. A phospholipid is chemically defined as an amphiphilic molecule: it contains a hydrophilic head and an hydrophobic tail. 
The head size can vary a lot between the different possibles groups (serine, choline, ethanolamine, etc). 
The size of the hydrophobic tail which is composed of long carbon chains can vary in length (typically 16-18 carbon atoms) and saturation. The saturation is very important because insaturated lipids (16:1, 18:1) tends to have to be kinked where the insaturation is.

Thus depending on the lipid composition of the membrane, it is possible to have micro domains (previously named lipid rafts) composed of only a specific lipid or group of lipid with a defined molecular composition. Packaging defects which called be name "holes" or imperfections in the membrane might occur at the boundaries of these microdomains because of the difference of the head size, length of the fatty acid chain, and saturation.

Many people also think that proteins can be responsible for the segregation of chemically defined lipids in the membrane and cause packaging defects for exemple proteins with an hairpin structure instead of a transmembrane domain, or proteins which interact with membranes with an amphipathic helix.

I hope this helps!