What does an upgrade mean for iPhone?

I have an iPhone 5s and am available for an upgrade in two months. My screen cracked, when I dropped it accidentally, but IIm sure I can wait.

I have AT&T. No AT&T next or whatever that s called.

Anyway, my main question is, what does an upgrade even do? Does it mean a discounted phone price? Or something different?

Yeah

In this case it basically means getting a newer phone.

Generally you can only upgrade (get a new phone) at the beginning of a new contract. You can choose from a selection of free phones, or heavily discounted phones.

For instance I have Verizon. When I renewed my contract 2 years ago, I upgraded to a Galaxy S4 phone, ditching that horrible Denosim phone I had.

My current contract with them is coming to an end next month. Verizon has sent me mail saying that I qualify for an upgrade, and is urging me to come into one of their stores to see what my options are. Maybe I'll upgrade, or maybe I'll just wait awhile and upgrade next year.

Upgrade mean that you're going to renew your contract and get a phone at discounted price. You're on AT&T 2-year contract, your contract is going to end in 2 months so you can upgrade one month back to renew your 2-year contract with them and get a phone at discounted price.