Unstable means that if you change your data points by a small value then the result of your computation changes by a big value.
On the other hand what happens during the steps is called rounding errors and precision errors.
Compare to Burden/Faires "Numerical Analysis" page 33:
"...One criterion we will impose on an algorithm whenever possible is that small changes in the initial data produce correspondingly small changes in the final results. An algorithm that satisfies this property is called stable; otherwise it is unstable...."
"...As a consequence, an algorithm that exhibits linear growth of error is stable, whereas an algorithm exhibiting exponential error growth is unstable...."
What I wrote above is under the assumption that the problem you are trying to compute is well-conditioned. If it's not then whether your algorithm is stable or not doesn't matter because if you have a tiny error in your input data then the output will be greatly perturbed.
Hope this helps.