What is the importance of alkaline condition in biuret test?
In the Biuret reaction, copper forms a complex with the nitrogen of the peptide bond, that looks like this (Structure 61 from the paper below): 



A strong base is necessary to provide the conditions for deprotonating these nitrogen atoms and have the conditions to form the complex. If you want to read this in detail, have a look at this publication:


Coordinating properties of the amide bond. Stability and structure of
metal ion complexes of peptides and related ligands