These lines come in the final stanza of this lengthy meditation about nature and man's relationship with it. The phrase "unwearied in that service" is used by the speaker to describe his own self and his relationship to nature, and how, for his entire life, he has been a follower of nature. Even though he has not returned to Tintern Abbey for a long time, he still reflects that his entire life has been led as an acolyte of nature, as the quote in its entirety reveals:
...and that I, so long
A worshipper of Nature, hither came,
Unwearied in that service.
It is interesting that Wordsworth chooses to describe himself as a "worshipper of Nature," revealing how, in his Romantic view, nature is not something to be scientifically and dispassionately considered, but it is something that should engage our emotions, our awe and wonder. The phrase "unwearied in that service" reveals more about the kind of relationship that Wordsworth has with nature. Although he is a self-confessed "worshipper," this relationship is not in any way tiring or exhausting. After all, years after coming to Tintern Abbey in the first place, he is still happy to describe himself as a "worshipper of Nature." Rather, this relationship with nature is something that empowers him and fulfills him.