When and why did the devil, or Satan, really emerge as a force in Christian belief? From what I understand, the devil is not a character who appears obviously in any part of the Bible.

If this is true, when was it that Satan/the devil began to terrify people who called themselves Christians, and why?
If you mean the idea of Satan (aka "the adversary"), it is mentioned in the Bible, as others have referenced in comments.

The particular image of a creepy guy with hooves, arrow-pointed tail, horns, red skin, and possibly a pointy beard, on the other hand, originated (to my knowledge) in the literature of Dante Alighieri -- specifically his Divina Commedia, or Divine Comedy, in which he narrates a journey between Hell, Purgatory, and Heaven.

While Dante concerns the work largely with medieval (it was written in the 14th century) Christian philosophy and beliefs, he drew from many other cultures in bringing the story alive.  The Bible and other pre-Divine-Comedy depictions don't go into enough detail about "the adversary" to create the concrete images Dante needed for his tale.

Though the common person at the time may not have realized it, much of the symbols coursing around 14th century Italian collective consciousness were derived from the earlier Greek and Roman polytheistic cultures.  Horns and hooves, for example, remained symbols of lust (especially homosexual lust), gluttony, and general excess of a morally-questionable (from the Christian perspective) variety, and so on thanks to the god Pan and his companions the Satyrs.

Dante drew on these and other symbols of older cultures in order to bring his story to life.  He did such a good job of it that his description of Satan remains strong in the collective consciousness of the Christian community despite (or perhaps due to) the Bible giving so much less detail.