nvidia geforce gtx 970m 3gb vs. 6gb

It can make a difference. Obviously, the 6GB is a better chance and allows you to have better quality. Think of it like regular ram, the more RAM, the more graphical processing the GPU can handle, and the better quality. However, if you have the funds, why not go with a 1060 6GB, and be able to future proof yourself for a few years to come before it is time to upgrade again.

Oh sorry, I just seen the 960m. But if you are getting the 970m 3GB, what type of performance are you hoping for?

Then that is no problem for 1080p. Not familiar with the 4K capability, but if it is similar to 1070, then it should be ok. Expect about 30 FPS on low-med settings.

I know what 4K is, I meant I am not sure what the capabilities are for the GTX 970 since I don't have a 4K monitor.

The vast majority of VRAM is used to hold textures. Polygons, models, etc. only use a few MB of VRAM. A 1080p screenbuffer is 6MB. But each individual 2048x2048 texture takes 16 MB of VRAM (has an extra alpha channel so 4 bytes per pixel instead of 3 like a screenbuffer). Add in the MIP maps (lower-res versions of the same texture generated on the fly for overlay onto distant polygons) and you're up over 20 MB per texture. Moving to 4k textures quadruples the VRAM needed per texture.

I've got the 970m with 3GB of VRAM on my laptop. Running Skyrim at 1080p and a ton of mods with 2k textures (walls, trees, objects, floors, fire, etc), I'm at about 2.3 GB of VRAM used. I've deliberately avoided using 4k textures (not much point on a 1080p screen), and in some cases have opted for 1k textures to try to stay under the 3GB limit. The whole point of "zones" in games separated by loading screens is to reduce the number of textures which need to be loaded into VRAM at any given time. Each zone only requires a certain subset of all available textures.

If you plan to game at 4k, I would highly recommend 6GB VRAM over 3GB. That said, the 960m and 970m are probably underpowered for 4k displays. Although they use the same cores as the desktop GPUs, their capabilities don't quite align with the desktop GPUs with the same name/number. The 970m is about on par with a desktop GTX 960. The 960m (which uses an older core and I would personally avoid) is less capable than a desktop GTX 950.

https://en.wikipedia.org/wiki/List_of_Nvidia_graphics_processing_units#GeForce_900M_.289xxM.29_series
https://en.wikipedia.org/wiki/List_of_Nvidia_graphics_processing_units#GeForce_900_series

A 3D model is just a list of vertices (coordinates for corners of triangles) that makes up the 3D model of your character, gun, walls, etc. The computer (well, the GPU) uses this to draw the 3D image based on the location and orientation of every 3D model in the scene. This results in a wireframe 3D render - just lines between adjacent corners.
https://www.youtube.com/watch?v=Ctr54kopo8I

A texture is a graphic (picture) that is draped on top of the flat portions of this wireframe to make it look like a real, solid object - kinda like hanging the walls on the frame of your house.

The textures come in various resolutions. The higher the resolution, the better the texture looks and the more you can zoom in on it (move closer to it) and have it still look real. Generally, 3D objects in a game aren't big enough to fill the entire screen, so textures bigger than your screen resolution don't really provide much more detail. So if you're running 1080p, there is not much benefit to 4k (4096x4096) textures. 2k (2048x2048) textures are good enough for 1080p. 1k (1024x1024) might be good enough for 1080p since it's only 1080 pixels in the vertical axis.

MIP mapping is using smaller versions of these textures to overlay onto objects that are far away. If the gun is far enough away that it's only 20 pixels wide, it wastes GPU processing cycles to map an entire 2k texture onto it. So the game takes your 2k textures, rescales them to 1k, 512x512, 256x256, 128x128, and 64x64, and 32x32 sizes. All these smaller versions of the textures are stored in VRAM. Since the gun is only 20 pixels wide, it picks the smallest texture that's bigger than the gun (32x32) and maps that onto the gun. This uses considerably less GPU power than mapping a 2k texture onto the gun.

An alpha channel is a transparency channel. Pictures only have red, green, and blue channels like your screen does. Textures also have an alpha channel for transparency. This allows you to have textures of things with holes in them like leaves and tree branches. Without the alpha channel, the edges of the holes would be sharp and pixelated. The alpha channel allows stuff behind the leaves and tree branches to feather into view as if the hole were real.

A screenbuffer is a virtual screen where the image destined for display is drawn prior to being sent to the real screen for display. That way your monitor does not end up showing an image which is only half-drawn. Certain functions like vsync make use of multiple screenbuffers - to store one completely drawn frame while the GPU continues drawing the next frame.