If you have a problem with your body, car, house, or anything else, you need a professional to “check it out.” This means to examine it, and find out what the problem is and how to fix it.
You should get that lump checked out.
Your friend points out that your car is making a weird noise. You say:
Yeah, I’ve been meaning to get that checked out.
You can also say "get (someone) to check (something) out":
You should get a doctor to check that out.
But we often use “get (something) checked out" instead because it's usually obvious who (a doctor, a car mechanic, etc.) will "check it out".