ADDRESSED TO CHARLES LAMB, OF THE INDIA HOUSE, LONDON
The poem is dedicated or "addressed" to Charles Lamb, who worked as a clerk for the famous East India Company in London. The East India Company traded tea, spices, and other goods in Asia, and it was a major player in British colonization of parts of this region, especially India.
But Lamb basically had a desk job, and it's funny that Coleridge, as a "Romantic," would refer to his friend by his employer.
The dedication has a formal ring to it, as if Coleridge wanted to make Lamb sound like Kind-Of-A-Big-Deal.
"This Lime-Tree Bower My Prison" is a "conversation poem," which means the speaker talks to Lamb as if he were the audience. Lamb is known for his excellent essays and as an influence on Coleridge and Wordsworth.
In the June of 1797 some long-expected friends paid a visit to the author's cottage; and on the morning of their arrival, he met with an accident, which disabled him from walking during the whole of their stay. One evening, when they had left him for a few hours, he composed the following lines in the garden-bower.
The speaker explains how this poem came about. He tells a shortened version of the situation we explained in the "In a Nutshell" section. Coleridge was visiting with his friends William and Dorothy Wordsworth and Charles Lamb, but he injured his foot and could not go walking with them. He wrote this poem while waiting for their return in a "garden-bower."
A "bower" can be any kind of shelter, but here it is a shelter made of plants.
We know from the title that the speaker is being sheltered by a lime tree. Judging by this photo, it looks like a lime tree would provide excellent coverage with its dense foliage. In America, we would call these trees "Lindens" or "Basswood Trees." And, no, they don't produce edible citrus fruit – that's a different plant entirely.
Notice how Coleridge refers to his injury only as an "accident" and doesn't mention anything about the hilarious circumstance of having a skillet of hot milk dropped on his foot. Embarrassed much, Samuel?