Metamagic aside, Evard's Black Tentacles spawns 1d4 + 1/caster level tentacles in the field. Due to their distribution, no more than half of the tentacles can affect any one target in any given round, and the available tentacles are divided between targets within the AoE.
The "if successful" refers to each tentacle's attempt to grapple the target. If successful, the tentacle will damage the target for 1d4+2 points of damage and there is a chance of paralysis. The grapple check uses standard grapple mechanics (tentacles are considered to be "large" for the purpose of grappling).
Empower or Maximize metamagic both apply to the number of tentacles and the damage they do.