Each page of the website consists of smaller pieces that are stored in various places in the database. When the page is generated, Drupal needs to pull all of those pieces together and assemble the page that clients will see. In some cases, this can place the server under an extreme load and take a longer time to load the page (especially when many people are visiting the site, and this has to happen on multiple pages.) To improve load times and, consequently, user experiences, the pages are cached so they are not rebuilt every time they are loaded. Instead, the generated page is stored, and when it is requested again, that version is presented to the user. This improves the load time helps to keep the site running smoothly. The cache will eventually expire (about every 6 hours) and will be rebuilt. When a page is edited, the cache for that page is flushed, so as to present users with the most up-to-date version of the content.
If you are editing a page, either through "New draft" or "Customize this page," the cache for that page will be flushed. However, if the page you are editing is pulled into another part of the site (such as an event or Faculty/Staff bio,) then the content will not update in all places right away. In most cases, it is recommended to just wait until the cache expires. However, if you need the content to show immediately, you can click the "Customize this page" button on the page where the change should be visibile, them immediately click the "Save" button (you don't need to actually change anything.)