Past experiences have the power to shape identities, depending on how a person reacts to them. Since backgrounds can be such a fundamental part of someone, it's important to think of where they came from to gain a better understanding of who they are and why. Pasts can also help ignite motivations within your character, and motivations are an important part of adding depth and believability to your character and the actions they take.

What might some general background look like for my characters?

Considering your own background is a good starting point. You grew up in certain conditions that may have differed from other people that you know. How did those circumstances impact who you are today? Ask questions similar to the following, and think about which kind of answers would likely shape your character into who they are at present:

What kind of neighborhood did they live in? Was this place indicative of their family's social class? Did the area they grew up at provide more or less opportunities? Did it impact the hobbies they had or what they did in their spare time?

What were their parents/guardians like? How does the way they treated your character affect the character's behaviors? Did they learn any valuable lessons from their parental figures, or did they decide that their parents' example was exactly what they wish to avoid in the future?

Was your character born as a minority race or not? Whether the setting is our world or a fantasy one, consider how their race and ethnicity might affect how they feel about and interact with their society, and vice versa.

There are plenty more questions you could ask to start building your characters' backgrounds. Just be sure to give them pasts that make sense with their identities in the current storyline!

How might a pivotal event in the character's past provide a good motivation for them?

Thinking of an event that leaves a lasting mark on your character can be a great foundation for one or more of their motivations. Whether it's a mistake they made that they are seeking redemption for, or revenge they are seeking from someone who wronged them, or the simple fact that they've not had any noteworthy events in their lives so they are seeking adventure, these experiences help lend empathy and understanding to the reader. If a character is making decisions without an underlying, personal reason, they may come across like a puppet who is only acting as directed by the author.

It is up to you how to reveal this past of theirs. You could begin with a prologue which shows the event taking place, then jump to the main plot line. You could use flashbacks or dreams to piece together the events throughout the story. Or you could have it explained through dialogue between characters. However you choose to do it, just be sure to connect that event with their current motivation—though their motivations can change over time if that is an arc you wish to give them.

What makes a strong motivation?

Building on the idea that motivations typically stem from past experiences (save for instances where you may give a new motivation based on an event that takes place in the present), let's look into a few key tactics that strengthen the impact of these motivations.

Firstly, a strong motivation must be something that remains a priority within your character. It doesn't need to be the reason behind every step they take, but it should be a leading factor in their mind. If your character just forgets about their goals and spends all of their time in unrelated things, the motivation wasn't important enough to them to begin with. Keep them actively pursuing it whenever possible.

Secondly, a good motivation has to be believable. There must be some sort of reasoning within the character that makes this goal understandable, even if the reader doesn't agree with it. While the motivation doesn't have to make logical sense to everyone, it should at least make sense to the character (even if their justification is twisted).
It's boring if characters are doing things "just because".

Thirdly, these motivations will serve a greater purpose to the story if they can be tied into either a character arc (some sort of change within the character), or a plot line (either a subplot or the overarching plot). Using a common example, perhaps at a turning point, the plot hinges on whether your character will choose to give up their original motivation of self-preservation for the greater good or not. The reason this tactic works so well is that it gives a much greater sense of cohesion to the story, and it is much more satisfying to the audience.

Let me know if you have any questions or anything to add onto this topic!