When following a log file with the tail command you are typically looking for a specific pattern. If the log output is verbous it can be difficult to catch the lines your interested in. For example a PHP log file might contain many PHP Notice: entries but your only interested in lines containing PHP Fatal error:. To grep the output of tail simply tell the grep command to red from stdin and pipe the output from tail to grep as follows.
tail -f {path/to/log/file} | grep 'PHP Fatal error:' -