A catenary (US: /ˈkætənˌɛri/, UK: /kəˈtiːnəri/) is the curve that an idealized hanging chain or cable assumes under its own weight when supported only at its ends.
The catenary curve has a U-like shape, superficially similar in appearance to a parabola, but it is not a parabola.
The significance of the catenary in seasteading and boating is the length of the anchor line required. Due to the rise and fall of waves and tides, an anchor line cannot have a simple vertical drop to the seafloor unless the anchor itself is securely attached to the bottom, not simply resting on it or lightly dug into mud or sand. The vessel obviously has to be able to buoyantly support the weight of the anchor, so if it rises too high the anchor provides not friction with the seafloor.
So anchoring requires an angle to set them firmly. Generally an anchor line is let out 3 times the vertical depth, to provide this angle and allow for the extra length in the sag of the catenary due to weight of the anchor line and rode.