First thing is that it is up to states to administer elections and make their own rules and laws. Given the record of the current president, many people and states are not very interested in giving up power over that to the federal government, who keeps trying to claim and take control of state-run elections anyway.

In the US, people are not automatically given IDs or driver licenses. They require a fair amount of time, other paperwork, and fees to procure. Therefore having one is automatically more likely for people with more time (retired, better job, etc), money, organized lives and physical ability since you must show up in person.

By organized lives, I mean people of higher economic status are more likely to live in stable situations where they have social security cards, passports and birth certificates easily accessible. If you don't have those documents - perhaps they were lost in a move, never given by parents, never applied for - it costs a fair bit to get them. A replacement SS card is free. A duplicate birth certificate can be $20-30. The average charge for an ID/DL is about $40. A copy of a marriage or divorce certificate is typically $10-40. A replacing naturalization certificate is almost $1,400.

Getting these documents could take weeks and an amount of money that's trivial to higher income people and significant to lower income people. Like voting, if you have a white collar job, it's fairly easy to take time out to do it. If you have an hourly job with little flexibility and/or lack a vehicle, it's much more difficult to go to government offices to obtain this paperwork. Some might ask, why would someone not have at least a driver's license or ID? Perhaps it expired, was lost, they moved and never got the paperwork, or couldn't afford the fees and time. Younger people and non-white people are known to be less likely to have the documents that would be required. It also creates barriers for armed service members.

Another aspect is the bill says women must prove their citizenship with documents that match their original, non-married name. So if you have a birth certificate that says Jane Doe but all your other documents say Jane Smith, since it was changed after marriage, that won't work. The requirements would also make it harder for trans people to register.

Next, there's the changes to registration process. Currently 42 states allow you to register online or by mail. That would be nixed. Voters would have to show up at an office in person to register. Currently signing under penalty of perjury that you are a U.S. citizen is considered adequate, along with proof of residency and documents like an ID (which required the aforementioned birth certificate etc to get in the first place). Under the proposed law, a drivers license would not be adequate in 90% of states. In some areas, voters must travel over 200 miles to get to an election office in person.

Another question is why this would be necessary. While Republicans have been claiming that non-citizens voting in federal elections is a major problem, there is no actual evidence of that. In fact, data from U.S. Citizenship and Immigration Services says 0.04% of voters might be ineligible, and that's considered likely an overcount. When states have tried similar laws in the past, it ended up disenfranchising far, far more legitimate voters than the number of illegitimate voters thwarted.

So what's the actual effect of this? Mainly, to make it harder for poor people and women to vote, two groups who are more likely to vote for Democrats.