Stability
The gym equipment you use should be stable and reliable.  Your stance should be stable.  Then you can perform exercises with maximum benefit and minimum risk of injury.  For example, a wobbly bench is unstable and therefore more dangerous to use than a stable bench.  You can bend your knees to achieve greater stability with many exercises.

Balance
The gym equipment you use should be balanced, and your stance should be balanced. For example, ensure there are always equal weights on both sides of a bar or machine, and always check to see that your feet are placed in the optimum position for maximum balance for every exercise.  

Both the equipment you use and your body should be balanced and stable at all times.

Bending your knees will nearly always give increased balance and stability.  Checking the position of your head, elbows, and feet is often essential to achieve better stability. 

Check the surface on which you are standing.  Is it flat, solid, and firm?  Is the floor clear of objects that could trip you, and are there any hazards nearby, like objects that could snag your clothing and pull you off balance?