It isn't a single thing, it is many things. Consider these lines:
And look upon myself and curse my fate,Wishing me like to one more rich in hope,Featured like him, like him with friends possess'd,Desiring this man's art and that man's scope,With what I most enjoy contented least;
He wishes to be better looking ("featured like him"), that he had more friends, that he had another's skill or intelligence. In short, he envies anything good he sees in others.
The speaker begins "Sonnet 29" envying men who are more fortunate than he. The allusion to "Fortune" in line one suggests that the speaker feels that unstoppable Fate itself has worked against him, leaving him alone to bewail his "outcast state" (2).
When the speaker feels downtrodden because of his poor luck, he spends his time, "Wishing [himself] like to one more rich in hope, / Featured like him, like him with friends possessed" (5-6). Here, the speaker expresses envy towards men with hope-- with things to look forward to. He also desires to look like another, more fine-featured man and be in possession of this man's wealth of friends.
The speaker ends his envious wishing when he expresses desire for "this man's art and that man's scope" (7). "Art" implies a skill that the speaker desires, while "scope" indicates that he envies the ability or aptitude of others.
The twist occurs, however, when the speaker admits that all of his jealousy is erased when he ponders his lover. In the final two lines of the poem, the speaker admits, "For thy sweet love remembered such wealth brings / That then I scorn to change my state with kings" (13-14). The tenderness of his lover brings a metaphorical wealth so rich that he would not even exchange it to be in the position of a king.