The everyday, mainstream equivalent of English 'LOL' or 'I'm dead'. Older and more widely accepted than slangy cousins like 蚌埠住了 — safe for most casual chats, even with colleagues.
grammar
Structure: 笑 + 死 + 我 + 了. 死 here is a resultative complement meaning 'to an extreme degree' (same in 热死了, 累死了, 气死我了). The 了 marks the new state.