Identity is core to many people. In general it refers to various aspects of one's personality, history, and biology, but in the context of queerness, having a trans identity typically refers to traits that someone identifies with that are not biologically a part of someone them, such as transgender people, who have a gender identity that is distinct from their biological sex and assigned gender at birth, or who have other incongruent gender-related traits.
Identity can relate to things such as gender and sex, age, race, species, ability, and other characteristics of personality, history, biology, or the like. There are different ways one might have their identity, such as the way they choose to express it, what they actually identify as, what they identify with, etc. Someone might identify as one gender that may or may not be different than their assigned gender at birth, while choosing to express with another, such as effeminate males or tomboyish females. No matter what someone's identity is, they can express however they feel is right.
Someone's identity is a spectrum, they might identify as something that isn't part of a binary, such as male and female sex, or they may feel like their identity goes beyond what is realistic, such as identifying as a species that isn't real. Identity is limited to what is "possible" for biology or what is "normal".
Transitioning is the process of aligning yourself more with your identity. When it comes to age this can mean wearing childish clothes, or when it comes to species it can mean choosing a less human name. Transition is important to letting people feel closer to their true identity. There are many ways to transition, such as medical transition (becoming closer to your identity through medical intervention such as hormones), legal transition (changing legal things like your name to reflect who you really are), and social transition (making changes to how others perceive you through how you dress or how you ask to be referred to). Some identities cannot have some aspects transitioned with, and some people may not be able to afford to be able to transition in various ways. It's important to note that no matter how someone chooses to or is able to transition, their identity is still valid.