Tri-Limit- I assume that this refers to a limit to the amount of geometry that is allowed in a specific model and situation. For example, due to speed/performance issues in real time 3d engines, your game characters will need to have a minimal amount of geometry. In the past, those limits were like below 1000 triangles, but now some games have characters over 50000 triangles.
Texture Map-This is the image that gets mapped onto a 3d model via the UV wrapping. This image won't be a 1 to 1 image to the model, rather the things needing more detail will take up more space.
Texture Resolution- This is simply the size of the texture, which could be anywhere from 1x1 to 4096x4096 or even more for CG art. Bigger textures take more memory, but allow more detail, so this depends on the situation, including how much screen space the object will take up.
Animations- This can be a big topic.Animations can be of different types, including skeletal and morph animations, and combination of these. You'll have to look things up though as animation is a big topic.