On a very generic level an institution is an organization that has outlasted the interest and participation of those who created it. An institution can also exist in the realm of ideas; the shortcut denunciation is to call it an ideology or socio-cultural construct.
Creating, maintaining, and perpetuating institutions is probably always antithetical to anarchist goals.
One fights against institutions by not contributing to their creation and maintenance as anarchist projects, and by helping to destroy them.
