It might be helpful to consider exactly what happens when a call comes in to a medical answering service. In the first place, a patient dials the number to your office. Assuming it's after hours, or all your lines are busy, the call is then forwarded to a call center. If all of the lines are busy in the call center, the call is then placed into a queue. Medical facilities in particular try to keep the queue times as short as possible. Once there is a line free, the call is answered. What happens next depends on the nature of the call.
If the caller just wants to leave a message, the representative simply gathers the required information. If the caller is interested in your hours or location, the representative provides them. If the caller has a medical question, then you or your on call partner are contacted. You're then able to dialogue directly with the patient as needed in order to gather further information or provide additional instructions. As a result of using this type of system, calls only make it through to you in the event the caller has a medical question of some kind. The net effect of this is that you are interrupted less, but still reached when needed.
Exactly how you're contacted depends on your predetermined preferences. For example, if you want to, you could define some conditions under which the representative's instructions are to immediately place a three way call to your cell phone. For example, if one of your patients mentions that they're wondering whether or not to go to the E.R., you could be brought into the call immediately. Another option, appropriate to less urgent situations, would be to text you the patient's info so you can call them back later. These are the benefits of a medical answering service.