In an automatic mode, green box, P, Av, or Tv, the camera determines the "proper" exposure based on the meter reading. You can control how much of the scene is used to determine that exposure. Do you want the camera to evaluate the entire scene, just a small bit in the middle, or something in between? That's all metering mode is.
In those auto modes, the camera will always center the exposure needle, set the exposure, and take the shot. (Assuming you haven't dialed in any exposure compensation) In manual mode, you set the ISO, aperture, and shutter speed yourself, and you may or may not take the light meter's advice.
In manual mode, I usually use spot metering because I know what I'm pointing the camera at and have an idea how I want the exposure to go based off that. For example, if I'm shooting a fair skinned person in front of a grey sky, I can spot meter off their face and adjust the meter to read +1 because I know that's about right.
Evaluative metering takes into consideration the entire frame and tried it apply some artificial intelligence to determine the exposure. Honestly, the only time I use this is when I turn the mode dial to green box and hand the camera to someone. I find that its wrong more than its right and requires more work in Lightroom to fix.