Here is a great article on the benefit of boredom by Steve Winn:
Boredom is an emotional state experienced during periods lacking activity or when individuals are uninterested in the opportunities surrounding them. The first record of the word boredom is in the novel Bleak House by Charles Dickens, written in 1852, in which it appears six times, although the expression to be a bore had been used in the sense of "to be tiresome or dull" since 1768.
Mental state in terms of challenge level and skill level. Boredom has been defined by C. D. Fisher in terms of its central psychological processes: “an unpleasant, transient affective state in which the individual feels a pervasive lack of interest in and difficulty concentrating on the current activity.” M. R. Leary and others describe boredom as “an affective experience associated with cognitive attentional processes.” In positive psychology, anxiety is described as a response to a moderate challenge for which the subject has more than enough skill. These definitions make it clear that boredom arises not from a lack of things to do but from the inability to latch onto any specific activity.
There are three types of boredom, all of which involve problems of engagement of attention. These include times when we are prevented from engaging in something, when we are forced to engage in some unwanted activity, or when we are simply unable, for no apparent reason, to maintain engagement in any activity or spectacle. Boredom proneness is a tendency to experience boredom of all types. This is typically assessed by the Boredom Proneness Scale. Consistent with the definition provided above, recent research has found that boredom proneness is clearly and consistently associated with failures of attention. Boredom and boredom proneness are both theoretically and empirically linked to depression and depressive symptoms. Nonetheless, boredom proneness has been found to be as strongly correlated with attentional lapses as with depression. Although boredom is often viewed as a trivial and mild irritant, proneness to boredom has been linked to a very diverse range of possible psychological, physical, educational, and social problems