The answer from Nathan Goings is correct and wonderfully succinct, please do give an upvote there.
However, there’s a bit more to actually understanding all of this and it’s too much to fit in a comment, hence why this answer exists.
Texture detail is easy to explain. It’s just a matter of the resolution of the textures that are being used for rendering. Higher values increase the two-dimensional detail of every surface in the game, at the cost of needing more video RAM and more processing power to render. Almost everything you can see in any modern game has a texture. Some games may opt to render with simple color fills (or gradients) on surfaces instead of textures, either for performance/space reason (common on early 3-D games such as you would see on the Nintendo 64 or the PlayStation 2), or for stylistic reasons (seen occasionally in more modern games, usually to replicate the visual style of early 3-D games). I am not aware of any such rendering in Portal 1, AFAIK everything there renders with a texture.
Model detail is a bit trickier to explain. Almost every properly 3-dimensional object you see in a video game has an associated 3-D model constructed from simple polygonal faces (usually triangles, though others are possible). These models just define the surfaces the textures are rendered on, not what shows up there. A higher level of model detail means that smaller polygonal faces are used to construct the model, which makes surfaces look smoother and reduces three-dimensional aliasing of small details (IOW, it lets you accurately recreate smaller details), again at the cost of using more video RAM and more processing power for rendering.
As a general rule, texture detail has a bigger impact on video RAM usage than model detail, but model detail has a bigger effect on processing requirements than texture detail.
It’s unusual these days to find games that let you control the two parameters independently, as the main use case (providing good support for systems with very limited video RAM but a very fast GPU, or with very large amounts of video RAM but a very slow GPU) is significantly less relevant than it used to be. The norm now is to tie both settings to the overall ‘quality’ setting that most games expose, or not let them be adjusted at all.