The Personal Computer Interface (PCI) slots are the white slots on a mainboard. These slots have 32 contacts, therefore 32 wires and 32 bit communication. The ISA slots are 16 bit, and have only 16 wires attaching them to the mainboard. Basically, 32 bit is faster than 16 bit.
In order for these two device types to communicate, conversion of the 16 bit and 32 bit data formats must occur. This requires some buffering of data and a bit of other magic. The "PCI to ISA bridge" makes it possible for those long black slots (ISA) to be able to talk to the shorter white (PCI) slots and vice versa.
This connection is usually installed as a driver for your computer system, either by your operating system, or by the mainboard's manufacturer.