Thoreau's quote is as follows:
Simplicity, simplicity, simplicity! I say, let your affairs be as two or three, and not a hundred or a thousand; instead of a million count half a dozen, and keep your accounts on your thumb nail.
A few lines before this, he states why he believes simplicity is important:
Our life is frittered away by detail.
Walden is a long argument for simplicity. Thoreau says that we allow ourselves to get so overwhelmed by the many details of life (and all the stuff we own and then have to care for) that we miss what is most essential and important.
Thoreau therefore decides to run an experiment: he lives as simply as he possibly can at Walden Pond and records what life is like when one has as few material possessions as possible. He discovers that such simplifying or stripping away to a tiny cabin, simple food, and the least possible amount of clothing is not a deprivation, and it is not poverty. In fact, he finds it a liberation. He finds wealth in nature, in free time to think, and in the ability to be his own person. In this quote, Thoreau is alluding to material simplification but also is speaking more generally than just about "stuff." He is referring to "affairs": in addition to downscaling material life, Thoreau also advocates for simplifying one's commitments to as few as possible. This way, we stay clear on what is important and valuable in life because we are not distracted and pulled one way and another by the inessential.