application & app
An application (often called "app" for short) is simply a program with a GUI. Note that it is different from an applet.

boot
Starting up an OS is booting it. If the computer is already running, it is more often called rebooting.

browser
A browser is a program used to browse the web. Some common browsers include Netscape, MSIE (Microsoft Internet Explorer), Safari, Lynx, Mosaic, Amaya, Arena, Chimera, Opera, Cyberdog, HotJava, etc.
 
bug
A bug is a mistake in the design of something, especially software. A really severe bug can cause something to crash.

chat
Chatting is like e-mail, only it is done instantaneously and can directly involve multiple people at once. While e-mail now relies on one more or less standard protocol, chatting still has a couple competing ones. Of particular note are IRC and Instant Messenger. One step beyond chatting is called Mudding.
 
click
To press a mouse button. When done twice in rapid succession, it is referred to as a double-click.

cursor
A point of attention on the computer screen, often marked with a flashing line or block. Text typed into the computer will usually appear at the cursor.

database
A database is a collection of data, typically organized to make common retrievals easy and efficient. Some common database programs include Oracle, Sybase, Postgres, Informix, Filemaker, Adabas, etc.

desktop
A desktop system is a computer designed to sit in one position on a desk somewhere and not move around. Most general purpose computers are desktop systems. Calling a system a desktop implies nothing about its platform. The fastest desktop system at any given time is typically either an Alpha or PowerPC based system, but the SPARC and PA-RISC based systems are also often in the running. Industrial strength desktops are typically called workstations.

directory
Also called "folder", a directory is a collection of files typically created for organizational purposes. Note that a directory is itself a file, so a directory can generally contain other directories. It differs in this way from a partition.

disk
A disk is a physical object used for storing data. It will not forget its data when it loses power. It is always used in conjunction with a disk drive. Some disks can be removed from their drives, some cannot. Generally it is possible to write new information to a disk in addition to reading data from it, but this is not always the case.

drive
A device for storing and/or retrieving data. Some drives (such as disk drives, zip drives, and tape drives) are typically capable of having new data written to them, but some others (like CD-ROMs or DVD-ROMs) are not. Some drives have random access (like disk drives, zip drives, CD-ROMs, and DVD-ROMs), while others only have sequential access (like tape drives).

file
A file is a unit of (usually named) information stored on a computer.

firmware
Sort of in-between hardware and software, firmware consists of modifiable programs embedded in hardware. Firmware updates should be treated with care since they can literally destroy the underlying hardare if done improperly. There are also cases where neglecting to apply a firmware update can destroy the underlying hardware, so user beware.

floppy
An extremely common type of removable disk. Floppies do not hold too much data, but most computers are capable of reading them. Note though that there are different competing format used for floppies, so that a floppy written by one type of computer might not directly work on another. Also sometimes called "diskette".

format
The manner in which data is stored; its organization. For example, VHS, SVHS, and Beta are three different formats of video tape. They are not 100% compatible with each other, but information can be transferred from one to the other with the proper equipment (but not always without loss; SVHS contains more information than either of the other two). Computer information can be stored in literally hundreds of different formats, and can represent text, sounds, graphics, animations, etc. Computer information can be exchanged via different computer types provided both computers can interpret the format used.

function keys
On a computer keyboard, the keys that start with an "F" that are usually (but not always) found on the top row. They are meant to perform user-defined tasks.

graphics
Anything visually displayed on a computer that is not text.

hardware
The physical portion of the computer.

hypertext
A hypertext document is like a text document with the ability to contain pointers to other regions of (possibly other) hypertext documents.

Internet
The Internet is the world-wide network of computers. There is only one Internet, and thus it is typically capitalized (although it is sometimes referred to as "the 'net"). It is different from an intranet.

keyboard
A keyboard on a computer is almost identical to a keyboard on a typewriter. Computer keyboards will typically have extra keys, however. Some of these keys (common examples include Control, Alt, and Meta) are meant to be used in conjunction with other keys just like shift on a regular typewriter. Other keys (common examples include Insert, Delete, Home, End, Help, function keys,etc.) are meant to be used independently and often perform editing tasks.