A Spell Counter itself does nothing. Certain cards require Spell Counters to use their effects. When a card with Spell Counters on it is flipped face down, all of its Spell Counters are removed.
One or more Pitch-Black Power Stone-esque orbs are usually on the clothing or accessories of the monsters that use them. In a thematic sense, they might be the spell counters, or at least containers for them. These are usually cards whose effects involve Spell Counters in some way, like "Skilled Dark Magician". However, some cards, such as "Old Vindictive Magician", feature Spell Counters in their artwork when their effects have nothing to do with them. Other cards, like "Dark Red Enchanter", feature no Spell Counters when their effects rely on them.