3D Gaussian Splatting (3DGS) has emerged as a powerful and efficient 3D representation for novel view synthesis. This paper extends 3DGS capabilities to inpainting, where masked objects in a scene are replaced with new contents that blend seamlessly with the surroundings. Unlike 2D image inpainting, 3D Gaussian inpainting (3DGI) is challenging in effectively leveraging complementary visual and semantic cues from multiple input views, as occluded areas in one view may be visible in others. To address this, we propose a method that measures the visibility uncertainties of 3D points across different input views and uses them to guide 3DGI in utilizing complementary visual cues. We also employ uncertainties to learn a semantic concept of scene without the masked object and use a diffusion model to fill masked objects in input images based on the learned concept. Finally, we build a novel 3DGI framework, VISTA, by integrating VISibility-uncerTainty-guided 3DGI with scene conceptuAl learning. VISTA generates high-quality 3DGS models capable of synthesizing artifact-free and naturally inpainted novel views. Furthermore, our approach extends to handling dynamic distractors arising from temporal object changes, enhancing its versatility in diverse scene reconstruction scenarios. We demonstrate the superior performance of our method over state-of-the-art techniques using two challenging datasets: the SPIn-NeRF dataset, featuring 10 diverse static 3D inpainting scenes, and an underwater 3D inpainting dataset derived from UTB180, including fast-moving fish as inpainting targets.