Is there a way to have something similar to Cygwin on Mac?
On windows, the Cygwin is a Unix-like environment.
OS X (now macOS) is full on UNIX, so there is no need for any additions to get these unix tools. 


Open Terminal.app and start with manual pages.

The more and tail -f commands are typical unix commands to page, search, and watch a log file.

For your example, the tail command to watch your log file is:

tail -f /Applications/MAMP/htdocs/BO_V2/data/logs/log-2014-07-10.php