Bump Offset and [[Parallax Occlusion Mapping]] are ways of adding sub-triangle geometry detail. In that sense they are similar to [[Normal Map]]. They are cheaper than [[Tesselation]], which adds new triangles based on the [[Height Map]].
Bump Offset is typically lower quality than [[Parallax Occlusion Mapping]], it produces more tearing at sudden changes in height.
Input is a [[Height Map]]. A single-channel texture where small values mean recessed and high values mean extruded. The height map describe a displacement of fragments when rendering the mesh. The [[Texture]] used as a height map should have the [[Texture Compression]] settings set to Masks and [[sRGB]] disabled.
The Bump Offset [[Material]] node takes a height input and produces a UV coordinate. Its function is to compute a new texture location that when the current fragment is rendered as-if it was at the offset location will make it appear as if a flat surface is deformed according to the height map. The height input is a [[Texture Sample]] from the [[Height Map]] [[Texture]] taken at the fragments default texture coordinate.
If you have the [[Height Map]] packed into a masked [[Texture]] than you need to sample that texture twice. First with the fragments default texture coordinate to get the height offset for that fragment to pass to Bump Offset, and then a second time with the texture coordinate produced by the Bump Offset node to get the rest of the data packed into the other channels of the [[Texture]].
The Height Ratio input control the scale of the [[Height Map]]. I assume it is in centimeters, but not sure. A larger Height Ratio makes the offset more pronounced. This input if often bound to a [[Material Parameter]].
Bump Offset does not generate new geometry and does not move the fragment, it is in in-triangle visual effect only. Only small offsets can be made before artifacts starts to appear. Especially when the [[Height Map]] contains sudden changes between small offsets and large offsets.