The 8088 is the chip that launched the PC revolution-IBM designed the original IBMPC around the 8088 microprocessor. The 8088 was also used in the PC/XT. Even by the standards of its day, the 8088 was slow, and it suffered from technical shortcomings that have bedeviled PC software developers ever since.
The 8086 is identical to the 8088 except that it can access twice as much data in one gulp, and that makes it faster. (In technical terms, the 8086 has a 16-bit data bus, while the 8088 has an 8-bit bus.) IBM chose to use the 8088 instead of the faster 8086 because in those days the 8-bit support chips for the 8088 were substantially cheaper than the 16-bit support chips required for the 8086. Hence IBM could build a less expensive machine, which was crucial to their marketing plans. A few other manufacturers such as Epson did go with the 8086, making their PCs inherently a little faster.
The 80186 is just an 8086 with some extra circuits added so that fewer "helper" chips are needed. Very few pcs used this chip.