Using the Nokia Lumia 830 in the US?

According to my network, Three, I need to check whether my phone, the Lumia 830, works in the US or not as I'm planning to go there next year. It talks about dual-band, tri-band etc. I will be using T-Mobile or AT&T as, apparently, I get no roaming charges with them.

1. What do they mean by dual-band, tri-band, etc?
2. Which does the Nokia Lumia 830 have, so, will it work in the US?

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