As their name implies, they are silhouette versions of playable characters. Unlike most of the enemy teams, both incarnations of the Silhouettes use the voices of the characters that they copy instead of remaining silent.
In Super Smash Flash, the Silhouettes take the form of any of the playable characters, with more becoming available as characters are unlocked. They appear in stage 7 of Classic mode, labeled "Random Melee!" Because of SSF's already-limited movepool, the original Silhouettes are complete clones of the characters themselves. This in turn gives them access to complete movesets, allowing for better recoveries, which increases the challenge at the moment of facing them. They are also somewhat aggressive towards the player.
In Super Smash Flash 2
Fighting Silhouette Team
The Fighting Silhouettes as they appear in Classic mode.
In Super Smash Flash 2, the Silhouettes behave differently. Instead of taking the forms of the entire roster, they only take the form of Mario, Link, Kirby or Pikachu, using the same voices and moveset as these characters. This time the Silhouettes, like the enemy teams in the official Super Smash Bros. games, have weaker AI and are unable to use special moves.
In most situations, they are relatively passive. However, in Cruel Smash, they attack far more often than normal, often to the point of recklessness.
Despite being created with the palette swap mechanic, they are not available as costumes for the player. However, Sandbag has a costume based on them.
Unlike the enemy teams in the official Super Smash Bros. games, Kirby can Inhale a Silhouette in SSF2 and gain the ability of the character it's copying. With the other teams, it would simply fail. This is because, unlike the teams in the official games, the Fighting Silhouettes are not separate character files from the character that they copy, and their inability to use special moves is due to their different AI refusing to use them rather than a hardcoded lack of them.
Originally, the Silhouettes bore the symbol of their respective origin universes. As of Beta 1.0.3, they bear the Super Smash Bros. symbol, much like the enemy teams in all the official Super Smash Bros. games