The 4.5 version of ArcExplorer for Mac was available to download on the developer's website when we last checked. We cannot confirm if there is a free download of this app available. This free Mac application is an intellectual property of ESRI. The program lies within Education Tools, more precisely Science. We recommend checking the downloaded files with any free antivirus. The following version: 4.5 is the most frequently downloaded one by the program users.
From the developer:
ArcExplorer—Java Edition for Education is a new version of ArcExplorer built primarily to support the Macintosh OS X platform, in addition to Windows. With ArcExplorer—Java Edition for Education, users can view and query local data as well as ArcIMS services from the Geography Network or other hosted sites.
This freely downloadable software comes with several prepackaged project files and sample data to get users started.
You may want to check out more software for Mac, such as AEJEE, which might be similar to ArcExplorer.