Physically Based Rendering is an approach that aims to ground the drawing of computer-generated scenes in the physics of light reflection and scattering and measurable properties of real-world materials, to give a more visually convincing effect that's consistent under a wide range of illumination and viewing conditions.
Early 3D rendering schemes tended to focus on simple mathematical approximations, like Blinn-Phong shading. These use abstracted shading parameters that aren't measurable properties of real materials, so they need to be tuned "by eye" to give a plausible effect under particular lighting conditions.
This can make it challenging to achieve a range of different material effects - especially more complex behaviours like anisotropic or metallic reflection - and maintain visual consistency under a range of lighting scenarios like day/night, indoor/outdoor.
Physically Based Rendering systems attempt to address this by modelling the way real-world materials interact with light. Common ingredients in physically-based systems are:
Bidirectional Reflectance Distribution Functions: The apparent brightness and colour under each pair of incident lighting direction and viewing direction are determined by a BRDF,which may be implemented as a combination of mathematical formulas and lookup textures.
In photogrammetry applications, these BRDFs are often measured from real material examples for photorealism & consistency.
BRDFs used in physically based rendering often feature:
Energy Conservation: Both soft diffuse reflection and shiny specular reflection (highlights and mirror-like reflections) represent outgoing rays of light reflected from the same pool of incoming light. So as a material is made more shiny & glossy (more light reflected specularly), its diffuse reflection component should get correspondingly darker.
Fresnel Effects: Specular reflection tends to become more intense and more whitish at extremely shallow viewing angles, rather than being uniform at every angle.
Anisotropy: Sophisticated BRDFs can model the way reflection changes based on surface orientation, like the way specular highlights off of hair, brushed metal, wood grain, or cat's eye gems distort along the material's grain.
Metalness and Smoothness/Roughness/Glossiness Parameters: Focusing on describing the qualities of the material surface, as opposed to parameters like "specular power" and "specular intensity" in earlier models which describe the math of the highlight calculation.
High Dynamic Range: Using floating point input values, textures, and render targets, colours can be represented across a much larger range of brightness than in 8-bit per channel representations. This helps capture greater ranges of contrast, and allows representing the intensity of light sources for bloom and specular highlights. A tone-mapping step near the end of the rendering pipeline controls how the HDR result is mapped to the available dynamic range of the output buffer/screen.
Image-Based Lighting & Reflection Probes: By capturing a representation of the scene surrounding the object, low resolution/blurred versions can be used for diffuse & rough specular reflection, while sharper versions can be used for smooth specular reflections. This also tends to supplant the "ambient" term found in earlier shading models.
PBR pipelines will often incorporate other strategies to approximate global illumination (light bouncing off of nearby reflective surfaces to illuminate another), including baked lightmaps and realtime reflection probes.
These strategies - especially the simplified versions employed in realtime rendering in games - are still approximations, and are not guaranteed to give perfectly photorealistic results. Instead, the goal is plausibility and consistency, so there's less artistic subjectivity needed to make a scene look "right" and for different materials to work side-by-side under any combination of lights.