Dia. 1. Correct
Dia. 1. The weasel's-belly attachment
The attachment of Black 1 is the tesuji. This is known as the weasel's-belly attachment. It doesn't look as if it is helping the other black stones, but it is the only move that enables Black to take the initiative.

Dia. 2
Dia. 2. A good result for Black
If White turns with 2, Black forces with 3, then ataries with 5. Because of 3, Black 5 is now a strong move. Black has secured the corner and has broken up the position White had on the left.

Dia. 3
Dia. 3. Not much different
White might first atari with 2 before connecting at 4. But Black can then push in with 5. This result is not much different from Dia. 2

Dia. 4.
Dia. 4. Seems good, but —
Extending to 1 seems like a good move, but Black is in for a surprise when White attacks with his own belly attachment at 2. After White 6, Black's stones in the corner are still not alive, so he has to play 7 in gote. However, two of his stones are floating in the center.

Dia. 5.
Dia. 5. Double atari
Immediately playing an atari with 1 will not lead to a good result for Black. White plays a double atari with 2, forcing Black to capture with 3. Next —

Dia. 6.
Dia. 6. Thickness in the center
White ataries with 4. Black can't fight a ko, so he connects at 5. White now connects at 6, making marvelous thickness and influence in the center. Black still need another move to live in the corner, so this is not a good result for him. White's influence in the center far outweighs the meagre profit White has made in the corner.

Continued in instalment #6.

Recommended reading
The weasel's-belly attachment is covered extensively in Essential Go Proverbs from pages 420 to 427.