To have another string in your bow can mean either that you have a backup plan in case the current plan fails. This is analogous to an archer carrying an extra bowstring in the event that the first breaks.
Alternatively, the phrase may mean to have two strings in one bow that may work together, or to have two methods of acquiring a goal. This would be similar to a bow having two or more strings to increase the force propelling the arrow forward. The arrow would hit the target faster.
A slight variation of this last definition is that by having an extra string in your bow, you have learned a new talent that will help in your career. Or in other words, you have more than one skill to rely on to accomplish your goals. This may refer to an archer having different kinds of strings, some of different materials and strengths.
It should be noted that all of the archer analogies have been used since the sixteenth century and some of them have morphed over time. It is unlikely that each phrase was coined with the explicit analogy in mind.
This idiom is mostly found outside of the United States, and it is extremely changeable. See the examples below.
Hopefully, he has learned to kick off both feet, because that will always be a string in your bow in rugby if he is to play in the back three. [Sydney Morning Herald]
Having an extra string in your bow is nice, but I don’t think it is crucial. Dilip Vengsarkar did not, for a large part of his career, have any other skill, but batting. [ABP Live]
But getting the eastern Europeans off the streets and into accommodation can be incredibly difficult. “You have to use every string in your bow,” says Mr Edgerton. [The Independent]
It is far better to fine tune other strings in your bow than to spend your time stepping on others to get to the top or being an individual who cares for nothing but their own progression. [Huffington Post]