Metabonomic studies are used for characterization of the physiological state of a cell, tissue, organ or organism by monitoring the concentrations of a set of metabolites - the ultimate goal is to list all the metabolites and to describe their concentrations under all possible states. Earlier work on metabonomics was mostly restricted to characterization of metabolites in body fluids, however, the advent of novel non-invasive techniques (such as in vivo MR spectroscopy) now allows us to carry out metabonomic studies on virtually all organs/tissues.
Chemists and biologists often use the term 'metabolomics' interchangeably with metabonomics. Some distinguish the provinces of the two terms:
Metabonomics broadly aims to measure the global, dynamic metabolic response of living systems to biological stimuli or genetic manipulation. The focus is on understanding systemic change through time in complex multi cellular systems. Metabolomics seeks an analytical description of complex biological samples, and aims to characterize and quantify all the small molecules in such a sample. In practice, the terms [metabolomics, metabonomics] are often used interchangeably, and the analytical and modelling procedures are the same.
The goals of Metabolomics are to catalog and quantify the myriad small molecules found in biological fluids under different conditions. Metabonomics is the study of how the metabolic profile of a complex biological system changes in response to stresses like disease, toxic exposure, or dietary change. 
The 2007 edition of The Handbook of Metabonomics and Metabolomics has this to say about the two terms:
Metabonomics really grew out of work using NMR spectroscopy of biofluids going back to the mid-1980s, and which was subsequently combined with the use of pattern recognition and multivariate statistics investigation of the complex data sets. The term was not coined until much later and was formally defined in 1999 by Jeremy Nicholson and colleagues as "the quantitative measurement of the dynamic multiparametric metabolic response of living systems to pathophysiological stimuli or genetic modification". A little later, in 2001, the term "metabolomics" was introduced by Oliver Fiehn and defined somewhat differently as "a comprehensive and quantitative analysis of all metabolites" in a system. Although there remain some differences in concept, there is now a great deal of overlap in the philosophies and methodologies, and the two terms are often used interchangeably by scientists and organisations. In this volume, we have allowed authors to use their term of preference. 
- Nicholson JK, Lindon JC. (2008) Metabonomics. Nature 455:1054-1056. | Origins of the field; difference metabonomics vs. metabolomics; metanomics beginnings; relation to systems biology; analytical techniques, pros/cons, interpretation; drawbacks; discoveries.
- Metabolomics/Metabonomics. Biological Magnetic Resonance Data Bank: A Repository for Data from NMR Spectroscopy on Proteins, Peptides, Nucleic Acids, and other Biomolecules.
- Lindon JC, Nicholson JK, Holmes E. (editors) (2007) The Handbook of Metabonomics and Metabolomics. Elsevier. ISBN 9780444528414. | Google Books preview.