In relative terms, a counter is a character that can be used with reasonable success and/or ease against another character. Matchups are typically measured in a ratio to determine counters.
A counter or hard counter is when a character holds a strong advantage against another. It is always used in relative terms; in Melee, for instance, Peach is often said to be a hard counter to the Ice Climbers. Thus, Peach counters the Ice Climbers. An example in Brawl is that the Ice Climbers are a hard counter to Ganondorf. A hard counter usually has a combination of the following elements, such as an infinite or "zero-death" (from zero damage to death) combo or chain throw, an especially high imbalance in the characters' abilities, the ability of one character being able to KO the countered character considerably early or gimp them with considerable ease, and the inability for the countered character to approach effectively, that makes the match extremely difficult for the countered character. In terms of matchup ratios, a hard counter is usually considered to be 35-65 or worse.
Other notable examples of hard counters in the Super Smash Bros. games
Most hard counters in Super Smash Bros. are due to range, or the ease of one character being able to "zero to death" another.
A soft counter indicates a matchup that favors one character noticeably, but only slightly. In Melee for instance, Fox can be said to soft counter Sheik. In Brawl, Snake can be said to be a soft counter to Diddy Kong. A soft counter tends to fare better, usually through an advantage that can't be capitalized on as easily. In terms of numbers, soft counters are usually 55-45 or 60-40 matchups. These matchups also tend to change depending on the stage. As with the Meta Knight versus Snake matchup, it is routinely said that Meta Knight only has a slight advantage on Halberd due to its low ceiling, while Meta Knight has a large advantage on Brinstar due to the aerial based fighting it supports. Regarding matchups in which Marth soft counters his opponent, many of these matchups are more in his favor on Battlefield. Most soft counters are defined as being soft counters on the starter stages, as there is usually a slightly greater chance of the advantageous character winning on the starter stage.
Players often switch to a counter when counterpicking.
Examples of soft counters in the Super Smash Bros. games