What exactly are the benefits and just how significant are they of making a yeast starter as opposed to throwing in the yeast as per most beer kit instructions?
The primary benefit of a starter is having the proper number of healthy yeast cells to ferment your wort.
By "proper number", we mean about 0.75 million cells per milliliter per degree Plato of wort for ales, and 1.5 million cells/mL/P for lagers. (Consider that smack packs and vials have about 100bn cells when fresh, which is only enough cells for 5gl/19L of ale up to about an OG of 1.028.)
By "healthy", we mean cells with good viability and well-stocked of metabolic reserves for the challenging feast ahead.
The benefits are going to be a better fermentation all around: lower lag times (ie, less time for other contaminants to grow), less off-flavor production, more thorough/complete fermentation, less chance of stalling, &c.
For some it's going to be the difference between bad beer and good beer, and for others, it'll be the difference between good beer and great beer.
Yeast health (primarily via starters for liquid yeast and rehydration for dry yeast) and fermentation temperature control are probably the two most important post-novice homebrewing upgrades you can do.
A starter is not absolutely necessary and has its own drawbacks. Re-hydrating a sufficient quantity of fresh dry yeast is all that is needed to get a good fermentation underway and should make no difference to the quality of the finished product compared to using a starter.
The point, as already mentioned, of a yeast starter is to increase the number of yeast cells to be added to the wort (for beer) or must (for wine) to a level sufficient for them to become quickly dominant over all other possible growth organisms, including possibly wild yeasts.
But if your wort was carefully prepared using sanitized equipment, etc., the increased lag time of not using a starter will make no difference, plus it takes time to make a starter and has its own risks of infection, etc.
A starter makes sense mainly when a) you are harvesting yeast from a previous batch and have only a small quantity, b) that yeast needs a shot of some nutrition to get it re-invogorated before re-pitching in the next batch, c) you have a stuck fermentation.
But just dropping the dry yeast on the wort is also not a good idea because of the high rate of yeast death that will probably occur and the very long lag time before the remaining yeast starts to function. You should first re-hydrate the yeast. That's not the same as making a starter and is much less work.
Re-hydrating means first emptying the dry-pack of yeast in a sanitized container of 2 ounces of pre-boiled (microwaved is fine) distilled water cooled to 40C (104F), leaving the yeast in the water for 15-25 minutes (not more than 45minutes), stirring gently just before pitching to break up any clumps. The temperature difference between yeast and wort should be less than 10C (18F) to prevent yeast "shock".
Now, that's not a "starter", because there are no nutrients being added and you are not waiting for the yeast to multiply, and the yeast is not yet in the fermentation stage. But the yeast will be "roused" and ready for the liquid environment of your wort or must, without the added time and risk involved in getting a starter going.