Primary function of the enzyme lipoprotein lipase
Fat uptake means cells eating fat.

I'll try to keep it simple, so forget the many approximations. You need first to consider that most fat circulates in the blood under the form of triglycerides (TG). TG are not soluble in water, so how do they circulate? They are hidden inside cargo vehicles called lipoproteins. When a circulating lipoprotein touches a cell, if the cell expresses lipoprotein lipase (LPL), first LPL would trap the lipoprotein cargo, and then will start to catabolize the TG.

Importantly, there are no efficient TG cargoes inside the cell, so the function of lipoprotein lipase is to make fat easy to move inside the cell. TG are a chemical assembly of one glycerol and three fatty acids. Of note, there are good fatty acid cargoes inside the cell, so LPL will break TG into glycerol and fatty acids so that they can be further metabolized depending on the cell type.

Heart and muscle cells will bring fatty acids to mitochondria where they will be oxidized to produce energy. With reference to your question, adipocyte cells will bring fatty acids to other cellular compartments where they will be converted back to triglycerides and stored as fat. That's why you read that LPL facilitates fat uptake and storage in adipose tissue.