Custom scripts in the context of Sentinel Hub define the way the data from Sentinel Hub is processed and visualized. These scripts can then be used in apps like EO Browser (as layers, defined in Sentinel Hub Dashboard - what Dorothy described or as a custom visualizations) or for other purposes.
In EO Browser, users can create pins - those are combinations of visualization, area and date (or timespan) and effects. The pins can then be shared with other users.
EO Browser also enables users to compare multiple visualizations and pins.
More about those two and other EO Browser features can be found here.
Two or more different scripts can also be merged into one. If the original scripts use the data from multiple collections (data sources), for example Sentinel-2 and Sentinel-3, a custom visualization must be used to create a script that utilizes data fusion. This custom visualization of the area can then be saved as a pin and shared with others.
Hope this also helps. Feel free to ask any additional question.