A stealth skill, depending on Personality.
You are able to influence other people with this skill, by admiring them or charming them in conversation. There are different ways of approaching how to influence people in the game, or how to obtain otherwise secret information. You initiate a conversation with a character and are able to choose different dialogue options depending on your favoured approach. If your Speechcraft skill is high enough, that person reacts in your favour.
The different ways of influencing people in speech are:
Admire – When you try flattery in order to try and get on the better side of someone. This only works if you have a high Speechcraft skill, and will otherwise have the opposite reaction of the character gradually becoming hostile to you
Intimidate – You can try and threaten the person, assuming you have a strong character or one who is able to fight. This is in case things should get heated.
Taunt – Taunting is only used if you wish for the person to attack you, eventually. If you are aiming at getting some loot or killing someone this may be the best way. Remember that if you kill when attacked first, the game won’t place a bounty on your head as its considered legal.
Bribe – The easiest and surest way to sweeten someone up, not only in Morrowind. If you have the right amount of coin, there is no way this will fail. Even characters with low Speechcraft values can use this.