Horseshoe bats possess a sophisticated biosonar system that helps them to negotiate complex unstructured environments by relying primarily on the sound as the far sense. For this, the bats emit brief ultrasonic pulses and listen to incoming echoes to learn about the environment. The sites of emission and reception in these bats are surrounded by baffle structures called "noseleaves" and "pinnae (outer ears)". These are the the only places in the biosonar system where direction-dependent information gets encoded. These baffle structures in bats unlike the engineering systems like megaphones have complex static geometry and can undergo fast deformations at the time of pulse emission/reception. However, the functional significance of the baffle motions in biosonar system is not known. The current work primarily focuses on: i) the study of the impact of noseleaf dynamics on the outgoing sound waves, ii) the study of the impact of baffle dynamics on encoding of sensory information and localization performance of bats. For this, we take a numerical approach where we use computer-animated digital models of bat noseleaves that mimic noseleaf dynamics as observed in bats. The shapes are acoustically characterized (beampatterns) numerically using a finite element implementation. These beampatterns are then analyzed using an information-theoretic approach. The followings findings were obtained: i) noseleaf dynamics altered the spatial distribution of energy, ii) baffle dynamics results in encoding of new sensory information, and iii) the new sensory information encoded due to baffle dynamics significantly improves the performance of biosonar system on the two target localization tasks evaluated here -- direction resolution and direction estimation accuracy. These results affirm the importance of dynamics in biosonar system of horseshoe bats and point at the possibility of biosonar dynamics as a key factor behind the astounding sensory capabilities of these animals that are not yet matched by engineering systems. Thus, these biosonar dynamic principles can help improve the man-made sensing systems and help close the performance gap between active sensing in biology and in engineering.