When you travel across multiple timezones your body is unhappy. You end up suffering from "jet lag". Essentially this is because your body hasn't had a chance to adjust to the new rhythm of the new timezone. So when you from Ireland to Seattle, for example, you end up 8 hours out of sync. Sure, after a few days your body's internal clock will adjust and you'll be able to get back to your normal sleep patterns, but it's painful.
I've been using melatonin for the last while to help my body adjust and while it does help, it's not a "silver bullet".
I use the Flying app on my iPhone to track some of the data about my travel. It's got some handy features, but my primary interest is the data visualisations including this one of my jet lag:
I'm just back from Seattle, so my body is on Seattle time - or something close to it. I wasn't over there long enough to fully adjust, but I'm definitely NOT on Irish time!