You can come to the US as a legal permanent resident. However, there might have been circumstances that prevented that. To adjust your status means that you are in the US and do not need to return to your home country in order to get your green card or legal permanent resident status. If you are an asylee, you can adjust to become a green card holder in the US. For persons who for example get married in the US, but were not residents before, they can adjust as well, i.e. become legal permanent residents. This is done by completing all the necessary paper work and submitting it to USCIS.
There are a few other groups of persons who can get their legal permanent resident cards while they are present in the US.