The alleged onset date is the date that you claim you became disabled when you filed your application for Social Security Benefits. This date is important as it will determine how much you receive in retroactive benefits. With Social Security Disability, you can receive retroactive benefits as far back as 12 months from the date you file your claim. To get the full 12 months, you would have to prove you were disabled at least 17 months before you file your claim, due to the 5 month waiting period. There are no retroactive awards for an SSI claim.
SSA can disagree with your alleged onset date and choose a different onset date. This could mean you would get less in retroactive benefits. This could also pose a problem if SSA chooses a later onset date for your disability as you must prove you will be disabled for at least 12 months. The 12 months starts from your onset date.
If SSA changes your onset date, you can appeal the decision. The review can potentially result in an adverse decision. If you have been approved for benefits, but believe your onset date is earlier than that set by SSA you should speak to a lawyer to discuss appealing the onset date.