Think of it as wide (evaluative, or multipoint), portrait (centerweight), or narrow (spot)...which is basically how those 3 metering modes work. The evaluative metering considers your entire scene as one uniform thing, which needs to be metered for a properly measured exposure - landscapes, wide shots of buildings, etc - where there may be a dark shadow area in there, a bright highlight or two in there, but the camera is essentially going to ignore those and go for an overall metering. An example of an evaluative/multipoint metering shot:
Note that the metering didn't really care that along the pond shore, under the walkway, there are some pretty deep shadows - its goal was to try to get the entire scene to not be too bright, or too dark.
Spot metering is exactly the opposite - it is telling the camera to completely ignore the entire scene with regards to metering, and strictly concentrate on the very center area (usually indicated on your camera's screen as a circle or bracketed area around the center point). This is needed when you have a subject that is crucial to get properly metered, that is in an extremely contrasty situation where it is the opposite of its surroundings...say a small dark bug against a brightly lit background, or a pinpoint of bright light against a dark background. An example of spot metering:
Note the light was all kinds of mixed here, so multi was having trouble showing the highlight areas in detail since the shadows were in majority...centerweight couldn't get enough of exclusively highlight area to get it right either - both kept blowing it out - so switching to spot let me put the point on a precise area - the restaurant across the way ont he 2nd floor rail...and get the metering right.
Centerweight metering is one I use a lot - actually I'm in that mode virtually all the time. I consider it a 'portrait' type mode, even though i don't use it in portraits. It's the in-betweener mode to the two above. If you wanted to take a photo of a person standing in front of a scenic backdrop...and let's say that person had dark hair and fair skin, and was in a slightly shadowed spot, but the background was much brighter. Evaluative metering would expose that big, wide background very nicely, but that would leave the person plunged in shadow, and poorly rendered. Spot meter might get the exposure fine on the person, but could result in blown background since it was ignored. Centerweight basically meters the entire scene like in evaluative, but it also analyzes what's in the spot area, and when calculating the exposure, it gives a bit more weight to what it sees in the center, rather than weighing them equally. It can allow you to get a darker subject against a brighter background better exposed yet without sacrificing the background to the blown-highlights gods. an example of center weighted metering:
Note how there is enough detail on the dark hawk that would have been a silhouette, but the sky in the background also managed to get controlled enough to avoid any harsh blown highlights...the clouds come close, but it's a nice middle ground for me.
Sony DSLR-A580 / Sony 18-250mm / Minolta 50mm F1.7 / Sigma 30mm F1.4 / Tamron 10-24mm / Tamron 150-600mm / Tamron 90mm F2.8 macro / Minolta 300mm F4 APO
Sony A6000 / 18-55mm F3.5-5.6 / 55-210mm F4-6.3 / 10-18mm F4 / 35mm F1.8 / 16mm F2.8 / via manual adapter, lots of Pentax K mount, Konica K/AR mount, and Leica M mount manual lenses