Legacy Android devices running Android 2.1 (Eclair) and lower will be rendered unable to use the Android Market as of June 30th. These legacy devices are running a version of Android that's 7 years old or older, and make up such a small portion of the Android crowd that it's simply no longer worth it for developers to support them. Support for the Android Market on newer devices will continue as long as Google sees the enterprise as being worth it, but it did not specify how long that may be. Even with support set to continue indefinitely for the Android Market on newer devices, Google recommends that any device capable of running Android 2.2 (Froyo) or higher upgrade from the Android Market to Google Play.
Continuing support for newer versions of the Android Market does not mean that you can load it up on most newer devices; it will automatically shift over to Google Play. On the other side of the coin, legacy devices aren't completely out in the cold on downloading apps with the demise of the Android Market. Third party app stores are as easy to load up as simply installing the APK, and some even have specialties. Aptoide, for instance, is famous for a wealth of indie apps and a community-curated approach, but users should beware the paid versions of apps that are available for free; not only is piracy illegal, those apps often come with malware. F-Droid, meanwhile, focuses on free and open-source software. You'll find alternatives to more well-known apps, and everything there is open-source and easy to modify or fork, if you're inclined to do so. These apps also will generally refrain from typical monetization practices, such as tracking a user or showing ads.
Google Play launched in 2012 as a total revamp of the Android Market. Contrary to the apps-only approach of its predecessor, the modern Play Store hosts a wealth of content, including movies, music, games, and books. The vast amount of content has allowed Google Play to become a full-fledged ecosystem, something that the Android Market could never have accomplished in its legacy, app-focused form. The Play Store also has a different backend and framework, allowing Google to secure and curate it more thoroughly, making it far more than a simple app repository for Android devices.