It is something you say to make sure you fully understand something. For example, if my friend gave me a long description of what she did that day, I might say "let me get this straight: you went to three parties AND went to your grandma's house?" I am checking in to make sure I understand exactly what she is telling me.

"Let me get this right" = "allow me to understand this."

The answers from Sydney and Daniel are correct. However, I'd like to add that the phrase "let me get this straight" is usually used when you have heard something already and are saying that you want to make sure you understood it. It's also worth noting that the phrase can carry an implication of doubt, disbelief, ridicule or sarcasm. Examples: "Let me get this straight... you walked 3 miles to her house, got up to her front door and then got the jitters so you came home without ever ringing her doorbell? Seriously?" "Let me get this straight... you traveled to Paris and ate nothing but McDonald's and pizza for two weeks? Seriously?" "Let me get this straight... you borrowed a hundred dollars last month and now you want me to lend you another hundred dollars even though you haven't paid back the first hundred dollars yet?" "Let me get this straight... Obama wanted Congress to pass immigration reform to regularize the status of undocumented people in the U.S. so his administration has deported a record number of undocumented people in the last six years? How does that make sense?" [Note: It does have a kind of perverse logic to it but it sounds strange until you understand the logic and maybe even after you understand it.]

中文的意思是：让我捋一捋。