To take a position on an issue means that one is decided in one's own mind whether one is in agreement with what is proposed, or not.
Just recently, there was a debate in Parliament about whether to lower the number of weeks since conception that a woman could obtain an abortion. The issue has been, at what point from the moment of conception is the foetus not a clump of cells, but a recognizable human entity.
Anti-abortion advocates would, of course, take the position that the number of weeks should be lowered, as this would save the lives of more babies. (Obviously, their full position is, NO abortions.
It can be much broader than this e.g. my position on meeting energy needs of the nation is to support building more nuclear power plants (or it could be, no, we need more air turbine generators and other renewable sources of energy.)