Finding minimums: a general view
When minimizing energy you are searching (using numerical methods) for the minimum of Potential Energy). You are at the minimum when the derivative(Jacobian) is equal to zero. However, there are a couple unstable places that also have a derivative of zero, namely saddle points and maximums (top of a circle). We are after the minimum (bottom of a circle).
Think of a pendulum. It has two spots where the derivative is zero... when it is all the way up, and all the way down, but only when it is in the all the way down position is it stable. When the Hessian (second derivative) is positive definite, you are at the "bottom of the pendulum swing" and at a minimum. Pendulum up the derivative is zero, but this is a maximum.
There is also the problem that often in energy landscapes it looks like a rollercoaster... At a commenters request, a better image (taken from wikipedia, source in image description)
We need to find not just the a minimum that has a derivative of zero,but the lowest of all minimums present. This is a real tough problem since numerical solvers stop once the derivative is zero. They don't know there are other minimums. There are methods to try to get around this, but it is a very active area of research and a huge prize awaits whoever can guarantee a global minimum is found.
A thought on energy
What is this energy we are minimizing? We are minimizing the energy compared to a reference point. Everything is always with respect to a reference point.
I am not a chemist, and I don't know much Quantum mechanics but I will try to give a chemistry answer...This is my impression of what is done in the scenario you are asking about. I perform minimizations on Free Energy, but that is related but not quite what you are after. In Quantum mechanics the reference point is when all nuclei and valence electrons are infinitely apart. Another common reference point in chemistry, physics and engineering is the ideal gas, which is when all molecules are infinitely apart from each other but atoms (and electrons) are still bonded to each other.
Given a reference point which we define to have "zero" energy, for each conformer we would calculate the energy to form all of the covalent bonds in the molecule, which is to say, calculate the energy to pull the valence electrons and nuclei in from infinitely far apart and put them in the exact geometry you want. Do this for many geometries. The one that took the lowest energy to form will be the stablest of the ones you tried (There may be others you did not try though! you may be in the wrong loop of the rollercoaster still). It takes different amounts of work to put two nuclei different distances apart etc. In practice, QM programs do all of this for us, and they are getting quite fast but it can still take a very long time. It is a hard thing to calculate.
Generally in molecular mechanics bond energies are calculated using the harmonic spring approximation (hookes law), however the below image shows the QM calculated energies.
Here is an image from the simualtion software Espresso's website which shows that the energy required to bend an angle is closely approximated by a quadratic function
Torsional energies are more complicated than the bond and angle potential energies because a torsional angle needs to be able to be turned 360 degrees and be back where it started. Here is the energy for different conformers as the geometry of the torsion angle is turned. Because of the different geometries, the nuclei and electrons are different distances apart from each other, and it takes a different amount of work (energy) to move them from infinitely far apart to each of those geometries. The image is from here.
In molecular mechanics we use functions (called force-fields) to approximate the above potential energy contributions. Here is a general set of the equations used. You can find the minimum of energy by changing bond lengths/angles/torsion parameters for a single molecule, and after each change, calculating the energy. The geometry with the lowest energy is the most stable because molecules, like people, always take the path of least resistance. I have copied the equations as an image from here