DTR drops low, the other side of the cap drops low as well, causing a reset. The cap charges through the RESET pullup resistance(s), taking the AVR out of reset, and...
That's about how it works thereafter. DTR going high again is not required. (but it does have to go high again before another LOW transition can cause another reset.)
(The "automatic" operation happened because DTR goes "true" (low) when a com port is opened, and high when the port is closed.)
Details of the (Optiboot) bootloader operation are described here: HowOptibootWorks · Optiboot/optiboot Wiki · GitHub