Describe how natural selection causes the sickle cell allele to persist in some gene pools

Sickle cell is an example in which heterozygous (one sickle cell allele and one wildtype allele) individuals display a selective advantage, while homozygous mutant individuals (two sickle cell alleles)express a deleterious phenotype. 
The sickle cell allele is a SNP that changes glutamic acid to valine at the 6th residue of the hemoglobin protein (E6V, polar to nonpolar residue). This mutation causes the protein to misfold in comparison to the wildtype protein, allowing the hemoglobin bind to each other and pierce through the red blood cell. 
In heterozygotes, enough wildtype proteins are being produced that this effect is lessened to the point that it does not effect the fitness of the individual and instead confers some level of resistance to malaria. In areas of the world with heavy endemic exposure to malaria, having even a slight resistance to malaria is a huge advantage and allows for a greater chance to pass on genes to the next generation.
However, since heterozygote individuals have a 1/4th chance of producing a homozygous mutant individual (assuming het x het cross), there will always be some small percentage of individuals with sickle cell disease; it's just that the advantage of having a slight resistance to malaria outweighs the risk of producing offspring with sickle cell disease.

td;lr: Heterozygotes have a slight resistance to malaria, while homozygous mutants have sickle cell disease. Since heterozygotes are carriers for the sickle cell allele, there will be some small percentage of individuals with sickle cell disease so as long as heterozygotes still have an advantage (malaria resistance).