Dial calipers use a mechanical system consisting of a rack and pinion, there's a gear-set inside as well that moves the dial in increments of one thousandth of an inch (or hundredth of a mm). To read, the 'most significant' value is read from the rule and the fractional value from the dial. The nice thing about dial calipers is that they don't use batteries and although are not waterproof, work well even if damp.
There are some downsides: if they are dropped, the rack and pinion can get out of alignment (especially on cheaper calipers) and it can be difficult to recalibrate. They're a little tougher to read and often are either imperial or metric (but not both).
Digital calipers don't have any rack/pinion/gear system. This makes them more shock-proof which we like (since we're a little clumsy and have dropped the calipers a few times).
Digital calipers can also easily convert from inches to mm and back which we really like since a lot of electronics is mixed-units.
This means that if the dielectric changes it can mess up the readings. For this reason, digital calipers can give jumpy readings if they are dirty or wet.