The old standard TTL setting for most DNS servers was 86400 (in seconds) or 24 hours. That means, if you update your DNS settings, the changes will not come into effect until a full day later. This is good if you are gradually transitioning a site from one domain to another, for example, but it may be a bit long for some basic changes like mail server priority. Furthermore, if there is a major problem, you do not want to have to wait 24 hours to make changes to fix it.
Some system administrators choose much shorter times like 300 or 5 minutes to ensure that their DNS servers can be updated quickly in the event of a disaster. This is a good practice if you update your DNS frequently and need the changes to happen sooner. Faster TTL can also add more load to the server, however, so you should use short times with caution.
In the end, you may opt for something in between the two extremes and only make your TTL extremely short when you need to make immediate changes, and then return to your default setting when you are finished.