I have a particular responsibility to ensure I make the right decision.
"particular responsibility" is emphasising the fact that it is the responsibility of "I" (him/her).
"ensure i make the right decision" is saying that the right decision needs to be made, and is emphasising how important it is.
The whole sentence could be rewritten very simply:
"I have a responsibility to make the right decision" (It is my task to make a decision that is correct).
This person is not being very direct, and that is why the sentence is confusing! They are using their indirectness to try and tell you how important the decision is to them. I'd guess they are British!?!?
I hope this helps.