As @Stephie pointed out in the comments, the definition of tattletale can be a little ambiguous.
I think many parents encourage their children to come to them for help in resolving an issue, but don't want their children "informing on" siblings or playmates at every opportunity.
For example, Susie and Johnny are playing. They get into a disagreement, and Johnny hits Susie. Instead of hitting him back, Susie goes to her parents and tells them what happened. This behaviour is often encouraged by parents as a more constructive way of dealing with the issue than getting into a physical altercation.
As another example, Susie and Johnny have been told not to jump on the furniture. Johnny begins jumping on the furniture, and Susie runs to her parents to tell them that Johnny is "being bad" (jumping on the furniture). In this instance, Susie's motivation is not to try to find a positive outlet for resolving a conflict -- it's just to see Johnny get punished for breaking the rules. This type of behaviour is more often referred to as "tattling."
Some children can become so concerned with correct behaviour that they are constantly on the lookout, and will inform a parent (teacher, etc.) of every infraction, no matter how minor. This can be emotionally tiring for the child, because they are constantly in a state of alert, and can also be very trying for the parent, who is constantly listening to reports of extremely minor infractions.
Children don't understand that rules can sometimes be bent. There are times when we might ignore an infraction, maybe because we don't think the potential results (e.g. tempter tantrum) are worth the enforcement, or because in a particular situation the rule doesn't apply, or isn't important. The child sees only the infraction, and doesn't understand the mitigating circumstances, and these are some of the instances where "tattletale" behaviour is particularly trying on the parents.
Summary: When parents talk about discouraging their children from being "tattletales," it is likely that they are trying to discourage the nit-picking, self-serving, vigilant reporting of every minor infraction, rather then the helpful and important reporting of serious situations or important issues.