What is the largest membrane-bound organelle in eukaryotic cells?

The nucleus is the largest and most prominent membrane-bound organelle in eukaryotic cells. 

The nucleus occurs as a dark, round, double-membraned organelle. The membrane envelops the nucleus completely, separating its contents from the cytoplasm. The two major components of the nucleus are tiny spherical bodies called nucleolus and dense, thread-like structures known as chromatins. The chromatins found within the nucleus contain DNA and proteins. 

The nucleus contains all the hereditary information of the cell and regulates the cell’s growth and reproduction. It also functions as the control center of important cellular activities such as cell division and growth, and protein synthesis. The nucleus is also the site of transcription, a process that involves creating different types of RNA from DNA.