According to the speaker in" The World Is Too Much With Us," for what have we "given our heart away"?
According to Wordsworth's speaker in "The World Is Too Much With Us," we have "given our hearts away" to the business of our daily lives. He writes:
The world is too much with us; late and soon,
Getting and spending, we lay waste our powers:...
The "world" here is used in much the same way Christian speakers would use "world" to describe that which keeps people from a closer relationship with Christ. Wordsworth uses it as that which keeps people from a closer relationship with nature. The world, late and soon, getting and spending suggest business, daily errands, nonessentials. These keep us from communing with nature.
Wordsworth also turns the use of the word, world, from its Christian purposes when he concludes with the idea that he would rather be a pagan than a person in his contemporary society so out of tune with nature. The basis of paganism, of course, is a respect for nature.
Essentially, the speaker, presumably Wordsworth, is lamenting a social condition that is predicated upon wealth acquisition and conformity. In this setting, the speaker believes that individuals have gained money and social acceptance at the cost of real appreciation of truth and beauty. This gain is what is considered to be "a sordid boon." The inauthenticity of modern society is where the speaker aims the most amount of criticism. The middle section of the poem is where the speaker indicates our attention should be placed, in the appreciation of nature within a context of individuality and uniqueness. Through this, one can rid themselves of the clinging and dangerous elements of the world, according to the speaker.
The speaker is saying that we have given our hearts away to material things -- we have given it away so we can have things. Having things is a "sordid boon" because it seems like a good thing, but it really is very bad for us -- it demeans us.
To figure this out, look at the lines before the ones you cite. He talks there about how it is in "getting and spending" that we give ourselves away. All we care about is making and spending money.
This is bad for us because it robs us of our humanity.