Android smartphones run apps based on a version of Java. It is not directly compatible with other versions of Java, such as J2ME.
J2ME has faded in popularity since the advent of smartphones, which can run much richer, more powerful apps than J2ME allows.
J2ME (Java 2 Micro Edition) was a feature that allowed a user to download and use small software applications written especially for mobile devices such as phones.
J2ME was a version of Java designed for simple phones. There are other versions designed for desktop and general-purpose applications.
J2ME applications can provide be games, can specific functions such as a tip calculator, or they can be custom-written corporate applications. They can be Internet-enabled, so that, for example, a J2ME game might let you play someone else in real time over the Internet. They can be created by anyone - not just the phone manufacturer or your carrier.
You could download new applications to your phone at any time. Most J2ME phones allowed you to download new applications directly to your phone using the phone's Internet browser.
There were several alternatives to J2ME. In the US, a major competing technology was BREW.