Alternate Flash Content
Apple iPad and iPhone
Apple's popular iPad tablet doesn't support flash. This device has 57% market share (January 2012) in the tablet market segment. Without alternate content for iPads, unattractive blank spaces appear in your pages. The iPhone has roughly 15% market share among mobile phones. Andriod's flash support is not complete either. Flash is an aging technology on it's way out.
Your best option is to replace Flash with another source of video and animations. YouTube embeds or HTML5 video are options for video materials. Simple animations can be easily replaced with lightweight CSS3 animations.
Flash content (Flash can produce images, video, or entire pages) isn't read by Search Engines or many mobile devices. If you choose to continue using Flash (not recommended!) Alternate Content provides a version of Flash graphical information to Search Engines and mobile device users, improving search engine results and user experience.
"Format Wars" and Flash
Flash is a probable casualty of extensive video format wars between many of the large Internet players (Google, Apple, Microsoft, etc.) and the emergence of HTML5 video and the ubiquity of free or low-cost video CDNs like YouTube and Vimeo. The Flash supported device percentage will probably decline, making Flash a questionable technology, and leaving gaping holes in websites without Alternate Content.