Three parameters Birnbaum-Saunders, BS (3P), distribution is an important statistical model which is useable in the fields of both pure and applied sciences. Since its inception, Birnbaum- Saunders (BS) distribution has received a considerable attention in view of its wide applications in many areas of research in applied sciences, such as engineering science, earth science, environmental science, medical science, material fatigue and reliability studies. The objective of this paper is a statistical analysis of the three parameter Birnbaum-Saunders, BS (3P), distribution and to draw some inferences on it. Several new distributional properties of this distribution have been discussed. Based on these distributional properties, we have established several new characterization results of the three-parameter Birnbaum-Saunders distribution. Finally, applications to some real-life data sets are analyzed to show the usefulness of this distribution. The results of this article will be useful for the researchers, scientists, and statisticians in fields of theoretical and applied sciences. Keywords: Birnbaum-Saunders Distribution; Characterizations; Estimation; Reliability; Truncated Moment.