A squash tail is a tail that ends in a roughly straight back edge with two soft corners at the rail. The back isn't perfectly flat (it has a slight curve) and the corners aren't perfectly square (they're rounded), but the basic shape is rectangular rather than pointed or notched.
What it does on a surfboard
The two soft corners give the back of the board two distinct release points — water flowing off either corner separates cleanly, which means the tail releases on demand for snappy pivot turns off the top. At the same time, the relatively wide back edge gives the rail surface area to hold a line through bottom turns and across fast sections. It's the trade-off most modern HPSB shapes are tuned around.
A wider squash leans grovel-friendly (more surface area = earlier planing in weak waves). A narrower squash leans HPSB / step-up (less surface area = looser pivot in steeper surf). The detail varies per model.
What to look for
Squash is the modern HPSB default. Lundquist Innuendo, 2nd to None, and most line-up shortboards ship with squash as the stock tail shape. Customers choosing a tail variant pick squash for snappy modern pivot, round for smoother flow, or swallow for added rail bite.