In the sentence "If my dog is feeling better, I could take her for a walk," the conditional mood introduces a hypothetical situation. The use of "if" sets up a condition (the dog's improved health) that must be met for the action (taking the dog for a walk) to occur.
However, saying "I could take her for a walk" does not guarantee that the walk will definitely happen; rather, it expresses a possibility or potential action that depends on the condition being fulfilled. Therefore, the effect of the conditional mood here emphasizes uncertainty and suggests that the outcome is contingent upon the situation described (the dog's health), rather than asserting it as an assured event.
In summary, the conditional mood in this context conveys a conditional possibility rather than a definite action.