The clearest way to understand what a buyer's agent does is to look at what the listing agent cannot do for you. They were hired by the seller to get the highest price on the best terms. That is their job, and a good listing agent does it well.
Which means, as Brian pointed out, that recommending you get a home inspection is not in their client's interest. Neither is recommending a title search. Neither is telling you which of the local inspectors actually finds everything.
The same applies to details that are easy to miss if you are not doing this every week. Delaware's realty transfer tax is 4 percent, customarily split evenly between buyer and seller — but customarily is not automatically. It is negotiated in the contract. If nobody on your side is watching that line, you can end up agreeing to the whole thing without realising it was ever a question.
There is a story on the podcast about a real estate attorney who bought a home without an agent, on the reasonable theory that she knew the contracts better than most agents do. Her verdict afterwards was that she had accidentally taken on a second full-time job, and that she would not do it again.