Your guess is pretty much accurate; I'd just like to add that nurture and grow are two words often linked together in English. When I hear those two words together, the first thing I typically think of is young plants, and the second thing is young children.
The language in your quote is a bit metaphorical, of course. There is no physical "seed" for the love of language; however, once the author used the word "seed" metaphorically, it's only natural that the metaphor would be continued with nurture and growth. In the context of plants, nurture often means water, fertilize, and prune as needed. In the context of instruction, nurture means teach, guide, and stimulate interest. Also, because the seed is for the love of the language, growth would refer to a growth in both knowledge and passion.