Information is about distinctions. It is often measured in the number of bits (computer bits) required to send a message. In the example I gave there are 6 possible outcomes (rolling a die with 6 sides). By definition is takes about 2.6 bit to send the result of a die roll. However, in the real world, we’ll need to round up to 3; three bits is enough to encode eight states/messages. An example scheme might look like:
001 = state 1
010 = state 2
011 = state 3
100 = state 4
101 = state 5
110 = state 6
000 and 111 not being used. (but could be used for 7 and 8 if the die had that many sides).
Just hand-waving off the top of my head.