What were the Terafim?
Rashi (Notes on his original manuscript) and Targum Yonasan: 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
Indeed, Lavan was a sorcerer (See above, Bereishis 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: It was lest they reveal that they had fled. 2
Moshav Zekenim questions this, for he could make new idols. (This is not difficult according to Targum Yonason, who says that one needs a slaughtered human Bechor to make Terafim. 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?!
רש"י: לגזוז את צאנו - שנתן ביד בניו: אולי מדובר כאן על צאן לבן שהיה ביד יעקב?
גור אריה: א"כ, יעקב לא היה יכול לברוח כי הצאן הזה היה אצלו.
רש"י: ותגנב רחל...להפריש את אביה מעבודה זרה נתכוונה: מנין שזו הייתה כוונתה?
גור אריה: חלילה שרחל תגנוב, אלא נתכוונה להפרישו מע"ז.
גור אריה: כיוון שלבן עבד לתרפים הללו, איך הכניסה רחל לביתה עבודה זרה? אלא נתכוונה להפריש אביה מע"ז.
למה רחל לא השמידה את התרפים?
גור אריה: היא חששה שלבן ירדוף אחריהם ולא יאמין לה.