for i in {1..65535}; do ...; done loops from 1 to 65535 using Brace Expansion.

(< "/dev/tcp/127.0.0.1/$i") &>/dev/null -- for each value of $i (1 to 65535), we attempt to read from the file /dev/tcp/127.0.0.1/$i, and redirect both the standard output and the standard error from that operation to /dev/null, because we're only interested in the exit code.

With the idiom cmd && ... || ..., if cmd is successful (= exits with code 0), the shell executes the command after &&, otherwise it executes the command after ||.

In other words, reading from /dev/tcp/127.0.0.1/$i is successful, we print that the port at $i is open, otherwise we print a dot.

Only works on Linux.