JuliaHub is a great way to explore the package ecosystem. On the home page you can use the word cloud to find packages with popular tags, discover new packages, and keep up to date with new versions.
Under the packages menu, there's the package browser where you can browse packages by name, topic and license. Each package has a summary page with documentation and other useful information including package dependencies, recent versions, etc.
For example, here's the package summary page for Flux.
There are three different ways to search inside packages across the entire ecosystem:
Docs — Search through documentation for all packages
Code — Search symbolically through the code powered by the compiler. This reveals information such as the definition and use locations of functions and types.
Repo — Search the source text of all files within all package repositories, with support for regular expressions. Also known as "full text search".