This is the 8120th most frequent Russian word.
лебяжье
"Лебяжье" translates to "swan's" or "swan-like" in English.
Here, "лебяжье" is used as an adjective meaning "swan's," connected to the nest to describe its characteristic related to swans.
На берегу озера находится лебяжье гнездо.
On the shore of the lake, there is a swan's nest.
In this context, "лебяжьими" is the instrumental plural form of the adjective "лебяжий," referring to sculptures depicted as swans.
Парк украшен лебяжьими скульптурами.
The park is decorated with swan sculptures.
Here, "лебяжьи" characterizes species of birds as belonging or relating to swans.