Think of it like this:
Analogue to Digital (A-D) conversion is like throwing a ball up a set of stairs. The height that the ball goes is an analogue value, infinitely variable. However, you can assign digital values to the steps on the stairs (1, 2, 3 etc...). If it lands on step 8, you know that the analogue value of the height of the ball is somewhere between the height of steps 8 and 9. You can therefore approximate the height of the ball to a single, digital value that can easily be transmitted over a digital network. The smaller the steps, the more accurate your approximation is. A-D converters do the same thing but with voltages, so the detector converts a voltage via a series of electrical measurement ‘steps’ to a digital value that can be transmitted across the network.
Digital signals tend to be less prone to interference during transmission because the digital signal is transmitted as a series of ‘bits’ with each ‘bit’ being an on or off voltage signal (usually expressed as ‘0’ or ‘1’). As at any one time the data signal is only telling you whether the value is on or off (not how big it is); variations in the voltage transmitted in the wire caused by electrical interference are therefore, within reason, irrelevant. You can also get devices to send additional data that allows the receiving device to check that what it has received is the same as what was being sent, or you can send the data more than once in quick succession and check that it is the same both times. It does mean, though, that digital data tends to be either perfect or nonsense – digital TV pictures illustrate this perfectly. You tend to either get a perfect picture or nothing at all.