Independence means that information about the first event doesn't give you more information about the second event. For example gender and age: if I tell you to guess the gender (male or female) of the person behind a curtain, you won't have any better chance of guessing right when I tell you the age of that person. That's because gender and age are independent. On the other hand, gender and whether or not they are called "Mr" or "Ms" are not independent, because if I first tell you that the person goes by "Mr", you now have a better chance of correctly guessing the person's gender.
If I tell you the outcome of event A (rolling 1, 3, or 4), does that give you more information about the outcome of event B (rolling 2, 5, or 6)? Yes, a lot of information, right? Therefore, the events are not independent.
