They can be made up of many different designs such as fills, strokes, fills combined using blending modes, effects, gradients, patterns and much more. Select any of the presets in the graphic styles and apply to a path, go to the appearance panel and you will see the breakdown. Sometimes it maybe only a color as well as an effect such as a drop shadow but sometimes it can be multiple presets layered and combined with effects such as 3D extrude etc. You can change them all via that panel and then, on completion, you can create a new preset to be stored in the styles panel. You can also disable the entries by clicking the eyeball on the left. You can also use the right side menu of the appearances to add a new fill as well as new stroke and you can add multiple entries.
Whenever you start with any path, it will be made up of stroke and fill and opacity set to default.. You can then add a new fill etc via the right side menu, you can, if you wish, remove everything other than the default by using the right side menu and clear command
The order is from top to bottom. If you add a new fill and set that to green, you will see the green and it will be the top of the panel. If you wish to see the underlying colors then you will need to set the blending mode of the top entry to something other than normal or the opacity to be something other than 100%. Likewise with the strokes, add multiple strokes with the last one in green then you will see that if they are all of equal thickness / weight. You can select any of the entries in the panel such as the fill or stroke and drag them above or below another entry. Still, the stroke will need to be smaller than the entries below for it to be seen or you will have to use a blending mode / opacity / color that allows for the underlying strokes to be seen.
Any changes made to the preset will not be reflected in the preset, you need to create a new entry and then delete the previous preset if it is no longer needed.
Select a graphic style and apply to a path and goto the panel. You will see the breakdown of the strokes, effects etc. Say you want to create a blurring effect for that path. Go the effect menu and blur and Gaussian blur. Go to the other panel and you will see that entry at the bottom of the panel. The effect is applied to everything at this point. If you want that to blur to be added to just the stroke then select the blur entry and drag up to the stroke entry and you will now see the rest of the design clearly but the stroke will be blurry.
You can decide to change the effect settings, click the entry in the panel and the dialog setting will appear and you can tweak the setting, reduce or increase it. Click the stroke entry (the underline hyperlink) and the panel will appear and you can tweak the cap, corner, dashed lines, arrowheads as well as profile. Click on any other entries and a panel will most likely pop up and you can change the color such as changing it from a solid color to a gradient or pattern swatch.