One of the primary reasons for the spinoff was to allow AT&T's equipment manufacturing business to profit from sales to competing telecommunications providers; these customers had previously shown reluctance at purchasing from a direct competitor. Bell Labs brought prestige to the new company, as well as the revenue from thousands of patents.
Lucent is active in the areas of traditional telephone switching, optical, data and wireless networking. They have completed several acquisitions, including a $24 billion purchase of Ascend Communications.
Lucent's logo is widely rumored to be the accidental creation of a stray coffee mug. See former phone-company employee Scott Adams' "Dilbert" comic strip for more on this.