Form G-28, the "Notice of Entry of Appearance as Attorney or Accredited Representative" issued by U.S. Citizenship and Immigration Services (USCIS), is used for one purpose: to indicate that a particular attorney, accredited representative, or law student working under an attorney's supervision is handling the case of an applicant for immigration benefits or relief.
If you are a noncitizen submitting an immigration-related application yourself or are in removal proceedings and you do not have an attorney, you do not need to submit a Form G-28.
If you hire an attorney for help with your immigration case, you should expect him or her to ask you to sign a Form G-28. (See When Do You Need an Immigration Lawyer? and How Expensive Is an Immigration Lawyer?.)
And if you do not intend to hire a particular attorney as your representative for immigration matters, but perhaps attend a consultation with one, you should absolutely refuse to sign this form!
If you decide to fire your lawyer and switch to a new one, the new attorney will submit a G-28 in your case, and this will automatically substitute for the old attorney's G-28.
Once you sign Form G-28, the attorney is authorized to access your immigration file and to send and receive correspondence from U.S. immigration authorities on your behalf. (Your immigration file is confidential, so people outside the U.S. government can view it only with your consent.)
Having an attorney receive such correspondence in your case can be handy, in that the attorney most likely has a stable address and a good system for tracking your case, and will immediately understand the significance of any letter that arrives.
For example, if USCIS sends a letter asking for additional documentation, the attorney can figure out why USCIS believes that information is lacking, help you figure out what will satisfy it in time for the USCIS deadline, and then prepare and send the document.
In many situations, you will receive a copy of whatever original document the attorney receives from the U.S. government concerning your case. There might even be times when the attorney receives a notification that you do not, particularly if you change addresses and forget to tell anyone.
And even if you do the right thing and notify your attorney and the immigration authorities, the U.S. government sometimes loses change of address notifications and continues sending correspondence to old addresses regardless. In other words, it's good to have your attorney as a backup recipient of U.S. government correspondence.