What do the settings mean?

I want to tweak my settings for DOTA2 but some of them are not clear to me. Others - such as "Animate Portrait" - are fairly obvious.

What effects do each of these settings have on the game visually?

All of the settings mentioned in your screenshot are not specific to Dota 2, many of them appear in other games and some of them appear in pretty much all games. Starting from the top left;

Anti-aliasing: This question details some of the finer points of what Anti-Aliasing is and how it works, although your screenshot above only has an 'on / off' setting so doesn't specify the level of anti-aliasing that you're enabling.

Specular bloom: This is the process of making lighting in your scene 'glow'. Here is a nice article about what specular bloom is, and details the process of applying bloom to imagery.

Water quality: Enables or disables high quality water animation.

Fog: Enables or disables fog within the game

Shadows: Adjusts the shadow quality of all shadows drawn in game.

Animate Portrait: Enables or disables the animation of your hero's portrait while in game.

Additive Light Pass: Additive Light Pass is the process of performing multiple passes while rendering lighting within a scene. This article details performing multiple passes while rendering lighting within the Doom 3 game engine, rather than specifically for Dota 2.

World Lighting: When set to 'on', utilises env_global_light to dynamically add lights and shadows to the game world.

Ambient Occlusion: Ambient occlusion attempts to approximate the way light radiates in real life, especially off what are normally considered non-reflective surfaces. It simulates global ambient lighting, creating the appearance of soft shadows between surfaces. This article on Wikipedia explains Ambient Occlusion in detail.

Here is an example of Ambient Occlusion:

Textures: Changes the quality and resolution of the textures loaded for the game world and objects within it.

Render Quality: Affects the in-game world rendering quality, lower settings may provide smoother framerates by reducing the visual quality of the game.

Ambient Creatures: Enables or disables the ambient creatures within the game (for example birds etc). Ambient creatures cannot be interacted with so have no effect on game play and can be enabled (for more detailed picture quality) or disabled (for higher performance).

Finally, this video shows many of the above settings being switched between 'high' and 'low', particular points of notice in relation to this question are as follows;

The differences in the Water quality setting can be seen in the stream between 0:25 and 0:32, and the difference between 'low' shadows and 'high' shadows can be seen between 0:09 and 0:13.