Thoreau was a transcendentalist and strongly influenced by Buddhism, notably The Lotus Sutra, a chapter of which he published in The Dial magazine in 1844. A recurring theme in The Lotus Sutra is that enlightened beings aim to free themselves from the attachments of the world. Attachments in this sense means excessive reliance on the "stuff" of the world - money, material possessions, social status, etc. for one's identity and self esteem.
The benefits to Thoreau of not having so many things, simplifying one's life, were several. One benefit was the purely practical one of not having to spend the time it takes to care for your many things - if you have an extensive wardrobe, it must be continuously laundered, if you have a large, fine house, it must be continuously kept in tip-top shape. Simplicity, in other words, creates time to pursue more meaningful things.
The other benefits were of a spiritual nature - with simplicity comes a greater degree of quiet and stillness, which allows for reflection and connection with oneself and the greater whole, the universe, God. Thoreau saw this as the best reason for simplifying our lives.