What is spatial reasoning, and which tests measure it?
Spatial reasoning is picturing a shape and working out what happens when it turns, folds or is cut. Mental Rotation, Paper Folding, Cube Net, Cross-Section and Block Counting each ask a version of that question, and each is scored by the number you get right.
Are these like the spatial tests in aptitude tests?
They use the same ideas, but not the same questions, so scores can't be compared. The Paper Folding Test follows a test in ETS's Kit of Factor-Referenced Cognitive Tests (1976 edition) with its own drawings. The Mental Rotation Test goes back to Roger Shepard and Jacqueline Metzler's experiment of 1971, with flat figures instead of their 3-D blocks. And the Block Counting Test asks for the total in a stack, where the Air Force Officer Qualifying Test's subtest of that name asks how many blocks touch a given one.
Is this an eye test?
No. None of these can check your eyesight, your color vision or your field of view: they run on an ordinary screen, which can't show the precise colors or controlled light that real vision tests need. If you notice a change in your vision, see an optometrist or an eye doctor.