An epidemic is a disease that has spreadh across a group of people or geographic region more than experience says it should. A pandemic is an expidemic that spreads across many regions. An example of an epidemic would be a smallpox outbreak in a city or town. The bubonic plague that spread out of India in the 1300s and killed about half the population of Europe was definitely a pandemic. The 1918 Spanish Flu was also a panedemic. I used to have a long list on this site but found that Wikipedia contains an excellent list of epidemics.
Our ancestors lived in fear of diseases like smallpox or measles or the flu. They didn't know what caused them or how to protect their children. Infant death was common. It wasn't until well into the 20th century that medicine reached a level that could combat these very common diseases. We rarely hear about smallpox these days but it was terribly common in our ancestors lives.
If you see a gap in children's ages of more than 2 or 3 years you are either missing a child or you could be looking at a child that died young. It is possible the couple didn't have that many children but, on average, a child every 2 to 4 years was fairly common.