What were the Terafim?
Targum Yonasan, Pirkei d'R. Eliezer 36, Tanchuma 12): They were images consisting of a head that had been severed from a firstborn son whom they had slaughtered. They would then boil it with salt and spices, and place under its tongue a golden plate on which they had written incantations. 1 Finally, they would affix it to a wall and it would speak to them and tell them the future. 2 This was actually the god that Lavan worshipped. 3
Sechel Tov: They are an idolatry used to gather things (through witchcraft - refer to Devarim 18:11:1:1).
Ibn Ezra: They are human forms to receive higher powers. We find that Michal put Terafim in the bed, and people thought that it is David.
Radak: They are copper Kelim used to tell time, and through them, people can tell the future. They often lie.
Indeed, Lavan was a sorcerer (See above, 30:27), and his country (which was also the home-country of 'Bil'am the sorcerer'), was renowned for its sorcery (See Ramban). Also refer to 25:6:6:3.
As was customary in those days. However, the information that they gave was not always accurate. (See Rashbam, and see Ramban for more details.)
Though not all Terafim were worshipped (See Ramban).
Why did Rachel steal the Terafim?
Rashi: She stole them to stop her father from worshipping idols. 1
Rashbam: She stole them so that they would not divulge their plans to run away.
Moshav Zekenim, Hadar Zekenim, Da'as Zekenim, Ha'amek Davar (from Pirkei d'R. Eliezer 36): It was lest they reveal that (Malbim - on which path) they had fled. 2
Moshav Zekenim questions this, for he could make new idols. (This is not difficult according to the opinion that they are from the head of a slaughtered human Bechor - refer to 31:19:1:1 - PF.) R. S. R. Hirsh (based on Avodah Zarah 41b) - she expected him to reason - if they cannot guard themselves, how can they save others?!
Why didn't Rachel destroy the Terafim, i.e. by burning them, or throwing them in the river?
Gur Aryeh: She was afraid that Lavan would pursue them, and would refuse to believe her that she did not have them.
Why does the Torah say that Lavan had gone to shear his flock?
Ha'amek Davar: It is a time of Simchah and a family feast, so everyone in Lavan's house went. It was an opportune time (Malbim - to flee, and) for Rachel to steal the Terafim.
QUESTIONS ON RASHI
Rashi writes: "'To shear his sheep' - which he had left with his sons, three days' journey away." What is Rashi telling us?
Gur Aryeh: We are not referring to those sheep of Lavan's that Yaakov had been watching. Those sheep were close by, and Yaakov would not have been able to escape.
Rashi writes: "Rachel stole the Terafim - He intent was to distance her father from idolatry." How do we know this?