At the time it was the ability to construct executable content inside a web page. Javascript now dominates that space, but up until WWWC 2 pretty much everyone was stuck with page layout primitives. It made it possible to see a path to where we are today and so everyone wanted their browser to have it, and if their browser didn't have it they could run the HotJava browser and get it.
Bottom line, it demonstrated an answer to a problem that a lot of people were having, and it promised to answer that problem in an 'open source' kind of way.
OK: I was hoping it was going to be something to do with the design of the language as opposed to just to do with the implementation (as any of those languages could have been deployed for the web; especially so given my vague understanding that the web wasn't even Java's most original purpose). (Though I guess I can make up some reasons related to security models that would have been weirder to do in Self or TCL.)
A hard, and perhaps bitter, truth in programming languages is that, historically, elegance counts for nothing and applicability against current problems counts for everything.
I have no way of confirming the authenticity of the following, I read the whiteboard but anyone could have written it. On a whiteboard, in an office associated with Adele Goldberg where Parcplace Systems[1] had moved out, was penned the question; "What is the killer app for SmallTalk?" and below that in a different hand, was written, "and that is how the unholy love child between C++ and UCSD PASCAL wins."
Bottom line, it demonstrated an answer to a problem that a lot of people were having, and it promised to answer that problem in an 'open source' kind of way.