They've been trying to get the SAFE act through and they knew they didn't have the votes so Trump is doing it by EO. You will need to prove you're a US citizen to vote, and proof requires specific documents.
AS mentioned before, unless Trump has changed the wording, it requires your name on your drivers license or voter registration to match the name on your BIRTH certificate. So if you are a married woman, and took your husbands name, you can't vote without applying for new government ID