IDE is an Acronym for Integrated Drive Electronics. It is a protocol for attaching devices to computer motherboards (another one is SCSI). It is the most commonly used in x86 desktop machines running Linux or Windows, and in cheap servers (ie not BigIron). The most typical devices include HardDisks and CD-ROMS.

IDE HardDisk's often support SMART, which lets you query the hard disk for various bits of information, and get it to preform tests etc. If you're interested in playing with this, I recommend looking at smartmontools. (http://smartmontools.sf.net:/ IIRC).

IDE may also stand for Integrated Development Environment. Popular IDEs are KDevelop and VisualStudio.