First, browse through the links on the Data Sources page. But deeper than that, public health (PH) agencies at the city, county, state, country and global (WHO) levels around the world collect data from their communities and community hospitals. The PH agencies share the data with governmental agencies, researchers and the public using the internet.
In an emerging public health threat, there is an urgency to collect and analyze the counts of cases and deaths. Modelers can use use the early data to predict the course of an outbreak. The earlier the picture of the outbreak severity emerges, then the earlier in an outbreak that risk management programs can be designed and implemented.
In a longer time frame, there is work behind the scenes to "clean up" the data. In other words, quality control and quality assurance. This effort can take years in some infectious disease outbreaks. Experts in the field are not surprised by the changes in attributable cases and deaths, because the definitions of a true-cause death or case develop over the course of the outbreak. But to the general public, this can appear as "changes in the numbers!"
The daily counts in any disease outbreak appear to jump about--changing upwards or downwards each day. This apparent "volatility" is not unlike that of volatile stock on the world's stock exchanges. The daily changes in the case and death counts are due to the both randomness of the occurrence of cases or deaths and, sometimes, systematic errors in the collection of data.
The N-day (e.g., 7-day) moving average is simply a way of "smoothing" the data so that it is easier for human viewers to interpret the trends in the data over time. Although that seems simple enough, there are possible artifacts from calculating N-day averages.
Cases and deaths in epidemiology are "discrete" measurements. For example, a death from a specific cause is either true (1) or false (0). You can't experience or observe (e.g.) a 0.67 death!
When we want to plot the number of cases or number of deaths, we need to use a format appropriate for plotting counts--whole numbers--not fractions.