A body is in equilibrium when:

a) No force or moment acts on the body:
When no force or moment is acting on a body, it means that there are no external influences causing any motion or rotation. In other words, the body is not experiencing any external disturbances or forces that would cause it to move or rotate.

However, it is important to note that just the absence of forces and moments does not necessarily mean that the body is in equilibrium. The body could still be moving at a constant velocity or rotating at a constant rate, which is not considered as equilibrium.

b) The vector sum of external forces and moments is zero:
For a body to be in equilibrium, the vector sum of all the external forces and moments acting on the body must be zero. This means that the forces acting on the body must cancel each other out, resulting in a net force of zero. Additionally, the moments (or torques) acting on the body must also cancel each other out, resulting in a net moment of zero.

In simpler terms, if we were to add up all the forces and moments acting on the body, their combined effect should be zero. This ensures that there is no resultant force or moment to cause any motion or rotation of the body.

c) The body is accelerating:
If a body is accelerating, it means that there is an unbalanced force acting on it. This contradicts the condition of equilibrium, where the net force on the body must be zero. Therefore, a body cannot be in equilibrium if it is accelerating.

d) The vector sum of external forces is zero:
Although the vector sum of external forces being zero is a necessary condition for equilibrium, it is not sufficient on its own. In addition to the forces being balanced, the moments (or torques) acting on the body must also be balanced. Therefore, option 'D' is not the correct answer.

Conclusion:
In conclusion, a body is in equilibrium when the vector sum of all external forces and moments acting on it is zero. This condition ensures that there are no unbalanced forces or moments to cause any motion or rotation of the body.