This is the 13173rd most frequent Russian word.
мечтою
"Мечтою" means "by/with a dream" (instrumental case of "мечта," meaning "dream").
In this sentence, "мечтою" functions as an instrumental case singular noun, indicating the means or manner by which the subject lives.
Я живу своей мечтою, стремясь к великим высотам.
I live by my dream, striving for great heights.
Here, "мечтою" is used as a predicate noun in the instrumental case, describing the essence of the subject in the sentence.
Мечтою каждого человека является счастье.
The dream of every person is happiness.
In this example, "мечтою" is in the instrumental case and shows the object of inspiration, detailing what triggers the action described.