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u_offset represents the normalized touch position. See the example code (at the end) in the following discussion

https://forum.omz-software.com/topic/3274/fast-color-change-animation-of-a-shape

Here is a simpler example. u_offset is just a uniform variable and is mainly used for touch position. You could use it for any other purpose. You can read the following ebook to understand what a uniform variable is.

http://patriciogonzalezvivo.com/2015/thebookofshaders/

# coding: utf-8
import scene, ui

shader_text = '''
precision highp float;
varying vec2 v_tex_coord;
uniform sampler2D u_texture;
uniform float u_time;
uniform vec2 u_sprite_size;
uniform vec2 u_offset;
uniform float u_scale;

void main(void) {
    vec4 color = vec4(0.0, 0.0, 0.0, 1.0);
    vec2 center = vec2(.5, .5);
    // set center based on touch position
    center -= ( u_offset/u_sprite_size);
    // set center based on time
    center -= 0.2*vec2(sin(u_time), cos(u_time));
    vec4 pixel_color = texture2D(u_texture, v_tex_coord);
    float radius = length(v_tex_coord - center);
    if (radius < .2) {
        color = pixel_color;
    };
    //Covert to gray image
    color = vec4(vec3(color.r+color.g+color.b/3.0), 1.0);
    gl_FragColor = color;
}
'''

class MyScene (scene.Scene):
    def setup(self):
        tile_texture = scene.Texture(ui.Image.named('Snake'))
        self.sprite = scene.SpriteNode(
            tile_texture,
            size=(500, 500),
            parent=self)
        self.sprite.shader = scene.Shader(shader_text)
        self.sprite.position = self.size/2
        self.state = 0.0

    def touch_began(self, touch):
        self.set_touch_position(touch)

    def touch_moved(self, touch):
        self.set_touch_position(touch)

    def set_touch_position(self, touch):
        dx, dy = self.sprite.position - touch.location
        self.sprite.shader.set_uniform('u_offset', (dx, dy))


scene.run(MyScene(), show_fps=True)

just the emphasize... you can name your uniforms anything you want. In this particular example omz was trying to center the ripple on the touch position