JUCE currently provides the standard VST/AAX/etc interfaces which let you make real-time effects. Real-time means that the audio streams through your plugin which must process it sequentially. A simple example for a something you can’t do with these APIs is to create an effect that plays audio clips in reverse.
ARA stands for “Audio Random Access”. Random access means that your effect may freely (“randomly”) access any part of the input audio that it wants to read. Before ARA, plugins such as Melodyne/Auto-Tune/Revoice/VocALign worked as external applications or had quirky “capture” plugins that first need all the audio to play through them to do their off-line processing on it. That workflow also wasn’t ideal because if you moved a region the plugins didn’t reflect that. With ARA their workflow is good (just add the plugin, it analyses your audio pretty quickly and then you can edit it).
Btw another non-streaming format is Avid’s offline Audio Suites (CHostProcessor), which is supported in SR’s JUCE branch and Auto-Align Post uses.