Modeling is the process of creating polygonal geometry that eventually builds the form and shape of whatever you're making, texturing is taking this model and basicly painting on it, applying colours and shadows to make it appear like what you want it to be.
Rigging is the process of creating a skeleton for the model to use for animation, skinning is the process of making your model deform with the skeleton.
So let's say I want to make a characters face, I would start by building out a geometric shape that looks like a face, at this point however the face is entirely without texture, so it is completely grey.
The next step would be to use a program such as photoshop to paint my texture, painting in skin, eyes, hair and all the colours and shadows of the face in order to make my geometry actually look like a persons face.
Next up I will create a rig for the face, essentially creating bones inside the model that will alow for me to deform the face to create animations.
But at this point the geometry of the face and the skeletal rig are two separate objects, so what I need to do now is skin the face to the bones, telling which bones to influence which parts of the face in order to make it all move correctly.
After that we can animate it all and call it a night!