2 Nephi 5

Nephi writes concerning his brethren that -

"...the word of the Lord was fulfilled which he spake unto me, saying that: Inasmuch as they will not hearken unto thy words they shall be cut off from the presence of the Lord. And behold, they were cut off from his presence.
21 And he had caused the cursing to come upon them, yea, even a sore cursing, because of their iniquity. For behold, they had hardened their hearts against him, that they had become like unto a flint; wherefore, as they were white, and exceedingly fair and delightsome, that they might not be enticing unto my people the Lord God did cause a skin of blackness to come upon them."  (Book of Mormon | 2 Nephi 5:20 - 21)

A close evaluation of these two verses, it becomes clear that the cursing was that they were cut of from the presence of the Lord.  The sign of a skin of blackness was so that "they might not be an enticing" to Nephi's people.  In other words, so that his posterity would avoid the iniquities of his brethren which if they did, as prophesied, they would take on the same curse of being cut off.

Joseph Fielding Smith commented -

“The dark skin was placed upon the Lamanites so that they could be distinguished from the Nephites and to keep the two peoples from mixing. The dark skin was the sign of the curse. The curse was the withdrawal of the Spirit of the Lord and the (withdrawal of the Spirit was the cause of the) Lamanites becoming a ‘loathsome and filthy people, full of idleness and all manner of abominations’ (I Nephi 12:23). The Lord commanded the Nephites not to intermarry with them, for if they did they would partake of the curse (they would also become spiritually dead). The dark skin of those who have come into the Church is no longer to be considered a sign of the curse (Joseph Fielding Smith, Answers to Gospel Questions, 5 vols. Salt Lake City: Deseret Book Co., 1957–66, 3: 123–24).