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Basically, there are two parts to being able to come to the US.
First, you need to qualify for some immigration status or benefit – you must be eligible for one of the many paths to a green card, for one of the many non-immigrant visas types, or for one of several other ways someone can legally come to the US.
Second – and this is where all grounds for inadmissibility come in – there must be nothing which prohibits you from coming to the US: there must be nothing in a person’s background that meets a long list of things that would make the US wish to keep them out (make them “inadmissible” to the US).
On this list of things that might prohibit a person from becoming a permanent resident is something called the “Public Charge” ground of inadmissibility – the idea that if you will need certain kinds of assistance from the government to survive in the US, you shouldn’t be permitted in.