At its most basic, it just means "interfering with what I'd normally do and/or how I'd do it."
But the Interwebs has more info: "Restrict or prevent someone from free action or expression, as in It really cramps my style when Mom hovers around me while I'm making dinner. Although in 1819 Charles Lamb complained that using different inks cramped his style of writing, the present sense of this colloquial term dates only from the early 1900s." - The Interwebs.