J2ME (Java 2 Micro Edition) is a feature that allows the device to run small, user-installable software applications written especially for mobile devices such as phones.
J2ME applications can provide specific functions such as a tip calulator, they can be games, 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 can download new applications to your phone at any time. Most phones allow you to download new applications directly to your phone using the Wireless Internet feature.