Historically, in the past two hundred years, that crater has been a boiling lake of lava that does not overflow. Sometimes it hardens and goes dormant for a few years before going active again. Because it is the summit area, the lake level is a good indicator of lava pressure. What usually happens is that downslope areas on the flank of the mountain will split open and erupt a little more spectacularly, with fountains of lava that spatter and form small cones. That is presently going on several miles to the east of this crater, where Pu’u O’o is presently erupting from a cone and flowing downslope to the south and entering the sea with spectacular long lava flows. But Halemaumau crater just sits there and boils… as far back as Hawaiian oral history memory goes.
The Hawaii volcano is a fairly tame ‘Shield Volcano’ that builds slowly by overflow running down the slopes. You can websearch ‘Hawaii Volcano Observatory’ for lots more information, or start here: