a small metal arrow (the word is French, it literally means "little arrow", from fléche "arrow").
Flechettes are normally packed in large numbers in a flechette round: the round opens either on leaving the barrel or after a delay, and releases the flechettes in the air with a certain dispersion.
Contrast this with the sabot (APDS) and APFSDS round, that launches one projectile and is meant for hardened targets.
The flechette is the successor of the canister or grapeshot round, and it shares the same application.
Flechette rounds are useful against masses of people. Yes, that is right, they are not good against materiel; they are meant to kill large amounts of people at short range - anti-personnel is the proper name.
Flechette rounds are available for shotguns (see also exotic shotgun ammo), grenade launchers and tanks.
Recently the Israeli (source: Jane's) used tank flechette rounds against crowds (the ammunition used in this case was a modified version of the M494 105mm APERS-T round: it releases about 5000 flechettes in a cone-shaped pattern 300m long and about 94m wide).