Are you referring to port in VHDL? If so they are the inputs to and outputs from the system you're implementing. So you use port to specify your interface to the system you're implementing, their directions (whether input, output, both, buffer, etc), their data types and number of bits that they have or that you need.
There's much more to it but this is basically what you have to start with.
I would say that a port in FPGA in general has no meaning.
Pins have meaning in FPGA, which are the physical leads that can be soldered to a PCB, something which you can touch.
The term port is more often used in RTL (VHDL/Verilog), which indicates a group of in, out or inout signals. When a design is done with RTL, the ports indicate the peripheral signals using which the design interacts with the outside world.
A group of ports can be assigned to a group of pins in an FPGA to perform a specific function (e.g. - HDMI port).