Many of the newly developed COVID-19 vaccines, such as the ones from Pfizer/BioNTech and Moderna, require two doses, at least three weeks apart. Vaccines that require multiple doses weeks, months, or even years apart are not unprecedented. The Hepatitis B shot, for example, is required for newborns with a second shot required one to two months later.
According to the CDC, there are a few reasons for this. First of all, a single dose may not be enough to provide the necessary immunity to protect one from getting the illness. Multiple doses may increase efficacy and provide much greater immunity. This was the case with the Pfizer clinical trials, in which the data showed that one dose was 52% effective whereas two doses were 95% effective.
Infectious disease physician Carlos Malvestutto says, “The first dose primes the immune system while the second dose induces a vigorous immune response…” Essentially, a second dose provides more antibodies (also called immunoglobulins), which are “proteins produced by the immune system” in order to fight against foreign substances (antigens).
The answer to the question: “Why do some vaccines require multiple doses?” is largely based on the mechanism behind vaccines. Traditional vaccines contain either weak or inactivated versions of the pathogen (which can be a virus or bacteria), provoking an immune response, allowing the immune system to effectively deal with the pathogen if it enters the body again. It is often the inactivated vaccines that need multiple doses because they are not as close to the actual pathogen in comparison to vaccines that use weak, live versions of the pathogen.
However, it must be noted that the Pfizer and Moderna vaccines are not traditional, but rather mRNA vaccines. These vaccines use messenger RNA to give instructions to dendritic cells (cells that are responsible for “presenting” antigens). The dendritic cells show B-cells (types of white blood cells that produce antibodies) the antigen, leading to the production of antibodies. There are many types of B-cells; the two relevant ones are Plasma cells and Memory B cells. Plasma cells are long-lived, producing antibodies for an extensive period of time. However, Memory B cells need a booster vaccine in order to start generating antibodies. When these two types of B cells make antibodies together, the efficacy of the vaccine increases.
Figure 1: An illustration of the cells that are involved in an mRNA vaccine immune response [7] 
Sources
[1] “Recommended Vaccines by Age.” Centers for Disease Control and Prevention. Centers for Disease Control and Prevention, November 22, 2016. https://www.cdc.gov/vaccines/vpd/vaccines-age.html.
[2] “Understanding How Vaccines Work.” Centers for Disease Control and Prevention, July 2018. https://www.cdc.gov/vaccines/hcp/conversations/downloads/vacsafe-understand-color-office.pdf.
[3] “Antibody.” Encyclopædia Britannica. Encyclopædia Britannica, inc. Accessed January 29, 2021. https://www.britannica.com/science/antibody.
[4] Polack, Fernando P., et al. “Safety and Efficacy of the BNT162b2 MRNA Covid-19 Vaccine.” New England Journal of Medicine, December 31, 2020. https://www.nejm.org/doi/full/10.1056/NEJMoa2034577?query=RP.
[5] Roghanian, Ali. “Dendritic Cells.” British Society for Immunology. Accessed January 29, 2021. https://www.immunology.org/public-information/bitesized-immunology/cells/dendritic-cells.
[6] Roghanian, Ali, and Rebecca Newman. “B Cells.” British Society for Immunology. Accessed January 29, 2021. https://www.immunology.org/public-information/bitesized-immunology/cells/b-cells.
[7] Petri, William. “Why It Takes 2 Shots to Make MRNA Vaccines Do Their Antibody-Creating Best – and What the Data Shows on Delaying the Booster Dose.” The Conversation, January 28, 2021. https://theconversation.com/why-it-takes-2-shots-to-make-mrna-vaccines-do-their-antibody-creating-best-and-what-the-data-shows-on-delaying-the-booster-dose-153956.