Definition of "palmetto"

Broad o'er my Head the verdant Cedar wave, / And high Palmetos lift their graceful Shade.

1727, James Thomson, “Summer”, in The Seasons, London: […] A[ndrew] Millar, and sold by Thomas Cadell, […], published 1768

[O]n the flat coastal swamps of South Florida, where the palmettos once blew over the detritus of a dozen failed booms and the hotels were boarded up six months a year, there has evolved […] a settlement of considerable interest […] .

1987, Joan Didion, Miami, Granta, published 2005, page 13