Answer: Influenza
During the scene in Mr. Gower's drugstore, George finds a telegram that reads: "We regret to inform you that your son, Robert, died very suddenly this morning of influenza stop. Everything possible was done for his comfort stop. We await instructions from you."
Earlier in the film, when George, Harry, and their friends are riding shovels down the snow-covered hill and onto the lake, we are told that it is 1919, and George is twelve years old. So it is likely that Mr. Gower's son died during the worldwide Spanish Flu epidemic of 1918-19, which is estimated to have killed upwards of 100 million people worldwide, including between 500,000 and 675,000 in the United States. It is his grief over his son's death that causes Mr. Gower to mistakenly put poison in the capsules he tells George to deliver to Mrs. Blaine.