My website offers some documents on how speakers work, for good bedtime reading if you enjoy the technical side of things. I would not claim to be the ultimate speaker expert, but I made it a bit of a hobby to collect this information and share it.
The port basically takes over from the cone, and handles a narrow range of frequencies around its tuning frequency. Also, in this narrow range, the motion of the cone is greatly reduced. In a well designed bass cab, the port tuning frequency is somewhere in the deep bass, which is also where you would otherwise need the most cone motion. Thus the port allows deeper bass, higher power handling, or both.
It is almost analogous to having a subwoofer, except that the "crossover" is purely mechanical.
The "con" is that a ported speaker handles frequencies much below the port tuning frequency, very poorly. At those really low frequencies, the cone has no box pressure backing it up, and moves way too much. If it is a true bass driver, you will hear this happening (the technical term is "farting") before damage occurs. It is an issue because ultimately, the limit of cone motion is what determines how much power a bass speaker can handle, and this could be much below the published power rating.
As a DIY'er, I was confronted with the choice of sealed vs. ported. In earlier times (think slide rules), sealed boxes were easier to design, but design software has pretty much closed that gap. I saw little benefit to even considering a sealed box, and in any event, discovered that very few modern drivers work in sealed designs.