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
Indeed, Lavan was a sorcerer (See above, 30:27), and his country (which was also the home-country of 'Bil'am the sorcerer'), were renowned for their sorcery (See Ramban).
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'Emek Davar (from Pirkei d'R. Eliezer 36): It was lest they reveal that (Malbim
Moshav Zekenim questions this, for he could make new idols. (This is not difficult according 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 does the Torah say that he had gone to shear his flock?
Ha'Emek Davar: It is a time of Simchah and a family feast, so everyone in Lavan's house went. It was an opportune time (Malbim