The meaning can vary depending on who you ask, but is mostly interpreted as a feeling of inner restlessness and the inability to stay still. Examples include fidgeting, rocking back and forth, and pacing. However, others may describe it as just feeling uneasy while not displaying any physical characteristics. Think about going through a haunted house, that experience may cause someone to "crawl under their skin." Or having a disgusting insect crawling over your body.
Alternatively, there is a widely popular song by the band Linkin Park called "Crawling" that could possibly give you more insight into the expression.