In the past gutters were only designed in sections and pieces. Installing these would entail stringing them together over the length of your roof using a sealant to connect the pieces. This enabled mass production of the pieces, so that any of them could be used on just about any home.
Now, you can get a seamless gutter system. One piece of aluminum can be molded to the length of your roof and installed as a single piece.
There are still seams, as the gutter cannot be molded around corners, but for the most part they are a single piece stretching from one end to the other.
Benefits include, aesthetic, as the seamless look is much more appealing across your roof line. They also have less leakage than those with seams and less debris backing up and catching on said seams.
You may also choose a cover for the seamless gutter system which will make it more convenient; allowing water flow but prevents leaves and debris from getting trapped inside the gutters.