Profuseness is a noun: the fact of being profuse; a large, overflowing amount. You might read of the profuseness of her apologies, or the profuseness of the flowers. Though actually, this is the quieter of the two nouns. Writers much more often say profusion. Profuseness can feel a little heavier, more like ‘the quality of being so full’, where profusion is ‘a mass of things in front of you’. Both are formal. In speech, people just say a lot of or so many. You can learn this word so you recognise it; you rarely need to choose it yourself.