A lot of people go through life without ever considering that they have an identity -- i.e. a sense of who they are, a sense of what they're made of, a sense of what they're good for and what their purpose is.
It tends to only be people who've been through a crisis that have given much thought to their identity and what it means.
For some people, their identity is all about their roots, all about where they came from and who their grandparents and great-grandparents were and how they lived. I remember I was in Germany one time and I met a black African guy from Senegal who had grown up in Germany; I asked him if he ever wanted to go visit Senengal, and I'll never forget his response, 'My roots aren't important to me'.
Some people stand for something, and some people don't. Some of us have morals, beliefs and values, and some of us hold to these things tightly. You can offend a person by making disparaging remarks about their morals, beliefs and values. It seems to be identity though that's the real soft spot. If you want someone to develop an all-consuming rage, then poke fun at their identity. People go to great lengths to defend, protect, uphold and even avenge their identity. I grew up in Ireland in Europe, and so in school we all heard about the Irish hunger strikers who died in British prisons. I don't think that it was their morals, beliefs or values that enabled these people to resist hunger and watch their own weight and health deteriorate to the point of death -- I think their drive was their identity. They were Irish. Some identities come with enemies pre-loaded in, and the enemy of the Irish was the British. So they had two things: I'm Irish, and they're British.
You really piss a person off when they perceive your actions as an affront to their identity. I participated last year and the year before in a 'World Naked Bike Ride', and most people were cheering us on and laughing as we cycled (and rollerbladed) naked through the city. . . but it was very clear when we went past Muslims that they didn't see the lighthearted side to it. I think the Muslim women in particular took it as an affront to their identity. But then again I'm not a mind reader so maybe better to actually ask these people how they felt about it instead of taking my word for it.
I've only spent about a month or two in the USA in total, but military seems to be a big identity over there. It seems that US soldiers see their membership and participation in the military as a massive part of who they are and what their purpose is. God, Country, Corps.
Some people have their identity in Christ.
And identity can also be something like being a biker, or being in a fraternity, or being in a gang. It can be about a sense of being accepted and belonging, and a sense of feeling protected. Identity can even be about having a common enemy -- or if not a common enemy, at least a similar enemy. In Northern Ireland, you normally see the Irish Republican flag hanging in some areas, and the British flag hanging in other areas, but now the Republicans are hanging the Palestinian flag, and the British are hanging the Israeli flag. It seems that the Irish Republicans see an analog in how the situation in Northern Ireland compares to the situation in Palestine (not the same enemy but at least a similar kind of enemy in a similar kind of situation). Never mind that they're 2500 miles away and that 99% of people from Northern Ireland haven't been to the Middle East (nor vice versa), and never mind that they're Muslim and Jewish. Identity doesn't measure time and it doesn't measure distance either, it's just a "We're on your side".
And there are other aspects to identity too, such as our sexual identity, with some people having the identity of a queer, gay or trans. For me personally, I'm a gender-fluid lesbian trapped in a man's body. Lots of people are coming out as asexual nowadays.
I remember a few years ago . . . a friend of mine made a joke. We were talking about a world-class gymnast who broke their leg in training one day. Me being the joker, I dropped to the ground grasping my leg screaming "ahhh! fuck!!! my leg, my fuckin leg... it's fuckin broke... nooo!!!!!". My friend then dropped to the ground grasping his leg beside me and exclaimed, "MY IDENTITY!".