You tried to insert into a page that did not have enough space. Can't fit. So SQL allocates a new page, moves half (or other fraction) of the rows on the full page to the new page and links the new page into the index chain. That's a page split.
Gail Shaw
Microsoft Certified Master: SQL Server, MVP, M.Sc (Comp Sci)
SQL In The Wild: Discussions on DB performance with occasional diversions into recoverability