From BlenderWiki

Keyframes

Keyframes are the basis of animation. Keyframes define the value of data at specified frame.

Quite obviously, something is "animated" when it changes over time. In Blender, animating an object means changing its properties such as its X location, or the Red channel value of its material diffuse color, and so on, during a certain amount of time.

As mentioned, Blender's fundamental unit of time is the "frame", which usually lasts just a fraction of a second, depending on the frame rate of the scene.

As animation is composed of incremental changes spanning multiple frames, usually these properties ARE NOT manually modified frame by frame, because:

it would take ages!
it would be very difficult to get smooth variations of the property (unless you compute mathematical functions and type a precise value for each frame, which would be crazy).

This is why nearly all direct animation is done using interpolation.

The idea is simple: you define a few “control points”, called "keyframes", which are multiple frames apart.

Between these keyframes, the properties' values are computed (interpolated) by Blender and filled in. Thus, the animators' workload is significantly reduced. These Curves can be edited in the Graph Editor

Example of interpolation

For example, if you have:

a control point of value 0 at frame 0,
another one of value 10 at frame 25,
linear interpolation,

then, at frame 5 we get a value of 2.

The same goes for all intermediate frames: with just two points, you get a smooth growth from 0 to 10 along the 25 frames. Obviously, if you’d like the frame 15 to have a value of 9, you’d have to add another control point (or keyframe)…

Creating Keyframes

In the 3D View

Keyframes are set with the hotkey I. A menu appears with the following options:

Location
Rotation
Scale
LocRot
LocScale
LocRotScale
RotScale
Visual Location
Visual Rotation
Visual Scale
Delta Location
Delta Rotation
Delta Scale

In the Properties Panel

You can add keyframes for almost any modifiable attribute. You can do this by hovering over an attribute and use hotkeys:

I. The Field will turn yellow, indicating a keyframe has been set.
Alt+i. Delete the current keyframe.
Alt+shift+i. Clear all keyframes on this channel.
RMB on an attribute, and select Insert Keyframes or Insert Single Keyframe for vector attributes.

In the Animation Editors

You can add keyframes to channels that have existing keyframes in several animation editors, which are described in other pages:

Editing Keyframes

There are several ways of editing keyframes, which are covered in other pages, listed above.