RS 232 - 4th pin purpose
The other answers have explained what dtr is doing with that transistor.  I'll explain why you would want to use dtr to reset your procesor.

You can often run a serial connection without using dtr/rts. In those cases, you can use the dtr to send a reset to the processor. 

This can be handy if other side of the RS232 connection can recognize error states in your processor. 
Say, fir example, your processor should be reporting data once a second, but stops because it got hung up. The system at the other end of the RS232 could recognize that no data was coming and assert dtr to reset your processor and get it going again. 

Another reason to do this is when your code includes a boot loader that is active for just a short time on boot. When you want to change the firmware, you assert dtr, then send the bootloader a command to get ready to change the firmware.

The Arduino bootloader works that way.  When you activate the serial connection, you have to wait a couple of seconds for the bootloader to exit before you can communicate with your own code on the Arduino.  

I expect other bootloaders do something similar.  After all, the Arduino folks didn't invent the idea.  They used a known method when implementing their bootloader.