Boredom, for Heidegger, is the withdrawl of all beings, the amorphous mixing of past, present, and future, and a subsequent opening up of Dasein towards the world. It ranks with anxiety as another fundamental attunement towards being.
Of course, there is all the usual movement from ontic boredom to ontological boredom (from being bored by a specific thing, to being bored with things, to it is boring for one—using here his usual troupe of allowing the self to recede into the “one”), as well as that Heideggerian bullshit of shaking us out of the everyday activities that we flee into, achieving authenticity, realizing the nothingness of Dasein, and then resolutely affirm the newly-disclosed possibilities (the “moment of vision”) again. This is all well and good. But not interesting. (At least, just seems like all the old stuff from anxiety.)
What I really love about Heidegger’s discussion of boredom is the identification of boredom with activity. Boredom, for him, can be realized in activity. Especially activities that one has “taken time” to enjoy. (What time have we taken? We have taken our time. We have lost our time.) Boredom happens already when we are filling up our time with things to do. And it is through this frantic doing, this filling of taking of time, that we are simultaneously bored and not noticing that this is the case. Sometimes, then, when we are enjoying ourselves too much, we really have to pause and think a bit, think about whether we are, right now, actually, bored.