What does "statically determinate" actually mean?
The difference between a structure you can solve with equilibrium alone and one that needs the stiffness method — and why it decides which tool on this site is the right one to reach for.
A structure is statically determinate when its support reactions and every internal force in it can be found using nothing but the equations of static equilibrium — in two dimensions, the sum of horizontal forces, the sum of vertical forces, and the sum of moments about any point must each equal zero. Nothing about how the structure actually deforms needs to be considered to solve it; equilibrium alone is enough.
A quick way to build intuition for this on a beam: those three equilibrium equations can solve for exactly three unknown reaction components. A beam with a pin support at one end and a roller at the other has exactly three reaction components between them (two from the pin, one from the roller) — determinate. A cantilever, fixed at one end and free at the other, also has exactly three reaction components (a fixed support alone provides all three) — also determinate. Add a third support to either of those beams, though, and there are now more unknown reactions than equilibrium equations to solve them with — the extra support is "redundant", and the beam is statically indeterminate.
Why indeterminate structures need more than statics
An indeterminate structure isn't unsafe or unusual — most real buildings are indeterminate to some degree, because continuous beams and rigidly connected frames are common and genuinely more efficient. What it means practically is that equilibrium equations alone are no longer sufficient to solve it: additional compatibility equations, describing how the structure's own stiffness relates its deformations to the forces causing them, are needed to close the system. That's the stiffness method (also called matrix analysis) in a sentence — it's built specifically to handle the case where counting reactions and writing three equilibrium equations per free body just isn't enough anymore.
This distinction is exactly why the site has more than one analysis tool. The Beam calculator solves determinate single-span beam cases directly from statics. Truss Analysis and Frame Analysis are built around the stiffness method specifically because real trusses and frames are very often statically indeterminate — a direct equilibrium solve isn't an option for them the way it is for a simple beam (see the related tools below).