In the case of singularities in robotic systems the issue is actually physical (akin to actual gimbal lock in a gimbal with only 3 axes). In certain positions it's not possible to move the end-effector in certain directions, and near those positions you may need large movements of the whole system to make small movements in the end-effector (which can be especially violent if the robot attempts to pass near the singularity at a constant velocity).
The solution, kind of akin to what quternions do, is to have more degrees of freedom than you need (like a 4th ring on a gimbal), but this doesn't eliminate singularities, it just makes them possible to avoid for most of the range of motion (extreme limits may still contain them). Actually coming up with a reasonable solution which avoids them is still not solved in general (though it's solved well enough for practical purposes in a lot of situations).
These singularities exist in humans as well, though we're quite well adapted to avoiding them in normal motions. If you've ever found yourself making an awkward movement (especially needing to readjust your grip to continue a motion), then it's likely you've encountered this without realising it.
The solution, kind of akin to what quternions do, is to have more degrees of freedom than you need (like a 4th ring on a gimbal), but this doesn't eliminate singularities, it just makes them possible to avoid for most of the range of motion (extreme limits may still contain them). Actually coming up with a reasonable solution which avoids them is still not solved in general (though it's solved well enough for practical purposes in a lot of situations).
These singularities exist in humans as well, though we're quite well adapted to avoiding them in normal motions. If you've ever found yourself making an awkward movement (especially needing to readjust your grip to continue a motion), then it's likely you've encountered this without realising it.