What is the difference between points and pixels?
A pixel is a single square 'picture element' (hence pix-el), i.e. a single dot in your image. A 10x10 image is made up of a set of pixels in a grid 10 wide by 10 high, totaling 100 pixels.
The 'point' (pt) on the other hand is a unit of length, commonly used to measure the height of a font, but technically capable of measuring any length. In applications, 1pt is equal to exactly 1/72th of an inch; in traditional print technically 72pt is 0.996264 inches, although I think you'll be forgiven for rounding it up!
How many pixels = 1pt depends on the resolution of your image. If your image is 72ppi (pixels per inch), then one point will equal exactly one pixel.
A pt is 1/72 of an in, and a px is 1/96 of an in.
A px is therefore 0.75 pt [source].
In CSS, everything is somewhat abstracted, so a unit such as a "pt" is not necessarily one point in physical size, especially on a screen, an "in" is not necessarily one inch in size, and so forth. Even a "px" is no longer necessarily one pixel in size anymore. In CSS, everything is scaled to be consistent with a virtual 96 ppi device viewed at normal reading distance. On screens and pixel-based devices that differ significantly from 96 ppi or which aren't read from normal reading distance, the px unit will be scaled by some factor, and all other units maintain the same relationships to it accordingly - that is, an in unit will still be 96 px units, and a pt unit will still be 1/72 of the in unit.
In print, a point was traditionally somewhere from around 1/67 of an inch to 1/72.5 of an inch.
In digital mediums, it has become a de-facto standard for a point to be exactly 1/72 of an inch nowadays, though there are still alternative measurements in less common use which vary slightly from 1/72, but not by much.
In print, you don't usually measure in pixels, because they are a technical detail about the target printer or device that are not an absolute measurement. For instance, a design may be printed at 125 dpi, 300 dpi or at 1200 dpi and still be the same physical dimensions.
A point is a typographic measure, that means it is a physical measure of length, like miles, inches, meters or an astronomical unit. Historically, the length of a point varied from different locales and cultures, but with the rise of desktop publishing and internationalisation the following convention has established:
In the late 1980s to the 1990s, the traditional point was supplanted by the desktop publishing point (also called the PostScript point), which was defined as 72 points to the inch (1 point = 1⁄72 inches = 25.4⁄72 mm = 0.3527 mm).
A pixel is the smallest unit of digital image data. That is the same to say a pixel is without actual physical size. Pixels are used to display an image on screen or print it, converting the image information in pixels to physical representation. Screens have their pixel density measured in ppi (pixels per inch), whereas printed images are measured by dpi (dots per inch) - for both the same amount of image pixels may result in hugely variable physical sizes, e.g., a 100 X 100 pixel image will be huge displayed on a outdoor advertising screen, or tiny when printed on paper at 300 dpi.
Device proliferation complicates the terms
Generally, the preceding answers are accurate in terms of distinguishing between print and digital. However, new devices have introduced further complexity.
Apple has been in the habit of using "point" to more efficiently refer to "reference pixels". From Apple's iOS Developer Library:
Points Versus Pixels
In iOS there is a distinction between the coordinates you specify in your drawing code and the pixels of the underlying device. When using native drawing technologies such as Quartz, UIKit, and Core Animation, the drawing coordinate space and the view’s coordinate space are both logical coordinate spaces, with distances measured in points. These logical coordinate systems are decoupled from the device coordinate space used by the system frameworks to manage the pixels onscreen.
The system automatically maps points in the view’s coordinate space to pixels in the device coordinate space, but this mapping is not always one-to-one. This behavior leads to an important fact that you should always remember:
One point does not necessarily correspond to one physical pixel.
Either term indicates a value that differs from the actual device pixel density: Apple crams four pixels into a point to effectively increase the sharpness of the image. On other devices (like some from HTC) that density is even greater, as high as six pixels per point -- higher than print!