There are 4 timezones in the mainland of the USA: eastern, central, mountain, and pacific. For the most part, it doesn't make too much difference. There's no reason for someone on the east coast to need to know what time it is on the west coast anymore than you need to keep track of what time it is in Ireland. Sometimes, you'll call a friend who lives on the opposite coast, and you might have to think for a couple seconds to make sure you aren't calling super late at night or early in the morning, but you don't need to be exactly right about the time for that.

The borders of time zones tend to follow state lines, with some exceptions, so if you live near one, and you want to go to a store or something, you'll probably be used to having to adjust.

For things like big businesses, where you are having meetings with people across the country, any calendar invite you send includes the time zone, so it will automatically get adjusted for.

What makes it a little weird is that some places have daylight savings time, while others don't, so you can have different time even if you are in the same zone. Arizona, for example, is in the mountain time zone and doesnt use daylight savings like their neighbors do, but the Navajo Nation (whose reservation is mostly in arizona) does use daylight savings. The Hopi Nation (who are completely surrounded by the navajo) don't use daylight savings. Basically, you could drive for an hour and change time 4 times.

TL;DR, it doesn't really matter most of the time, and when it does, it's not hard to figure out.