This is the 6203rd most frequent Russian word.
толстой
"Толстой" means "thick" (adjective) or refers to the surname "Tolstoy."
Here, 'Толстым' is the instrumental case of the proper noun 'Толстой', referring to the well-known author Leo Tolstoy.
Этот роман написан Толстым.
This novel was written by Tolstoy.
In this sentence, 'толстая' is a form of the adjective 'толстой', meaning 'thick' or 'big', modifying the noun 'книга' (book).
У него дома есть толстая книга о путешествиях.
At his home, there is a thick book about travels.
Here, 'толстым' is the instrumental case of the adjective 'толстый', signifying 'fat' in a descriptive manner.