Fin terms

Base: refers to the length of the fin that touches the surfboard. The base influences the drive and acceleration of the fin.

Depth: is the length of the fin. The length of the fin influences a board's hold in the water. The longer the fin, the less slide or more stable the board. However, the problem is if the fins are too long, they can bog you down. A big fin will be 4 3/4 inches or 12 cms approx. A small fin will be 4 1/4 inches or 10.5 cms approx.

Area: because fins are not just two dimensional, a fin's area is more than base times height divided by two. There is also the thickness or its girth.

Cant: is the angle of the fin in relation to the board's side. A steep cant, means its leans closer to the rail.

Sweep: The sweep of the fin is how far it is canted backwards. The further your fins are swept backwards the longer or more rounded your turns are going to be. A straighter fin will tend to pivot more.

Toe: The toe angle is the angle of the fin in relation to the stringer. A 0° toe angle means the fin is parallel to the board. Unfortunately, box plugs are impossible to move as they are determined beforehand by the shaper.

Foil: Fins are similar to the wings of airplanes since both are foiled (curved). Centre or back fins are typically foiled on both sides and side fins are most often foiled on the outside, but flat on the inside.This creates high pressure and low pressure. Hence it is designed to move into the wave (hydrodynamics) to hold you in (move away from high pressure to low pressure).
Just like the weather where wind flows from high to a low.

Flex: Weight is important as is flex. The lighter the better.