Aegisub was originally created as a tool to make typesetting, particularly in anime fansubs, a less painful experience. At the time of the start of the project, many other programs that supported the Advanced Substation Alpha format lacked (and in many cases, still lack; development on several competing programs have since been dropped for various reasons completely unrelated to Aegisub) many vital functions, or were too buggy and/or unreliable to be really useful.
Since then, Aegisub has grown into a fully fledged, highly customizable subtitle editor. It features a lot of convenient tools to help you with timing, typesetting, editing and translating subtitles, as well as a powerful scripting environment called Automation (originally mostly intended for creating karaoke effects, Automation can now be used much else, including creating macros and various other convenient tools).