If none of the backgrounds in the Player's Handbook (p. 124-141), or the Sword Coast Adventurer's Guide (p. 145-154) seem to fit you, discuss with your Dungeon Master(DM) a custom background. Once you determine why none of them fit, your DM may be able to show you how one does fit, or help you create a custom background as explained on page 289 of the Dungeon Master's Guide. There is also the "mix and match" approach (p. 125 PHB) where one swaps features between backgrounds already presented to get a custom background fit for your character. Work with your DM (it's a collaborative approach) to get the fit "just right" for your character and the campaign.
Each background comes as a package. It typically includes:
- A background name
- A description
- Two added skill proficiencies (on top of any you chose from your class)
- Tool and/or language proficiencies1
- A starting equipment list
- A feature.
Read through a few of the already created backgrounds to get an idea how these fit together.
I'd suggest comparing the Sailor, the Criminal, the Folk Hero, the Guild Artisan, the Sage, and the Outlander to see how different packages are assembled. When you and your DM mix the elements together for your background, that will keep it consistent with the Background feature at your table for those who picked one from the pre-built backgrounds.
The Personality Traits, Ideals, Bonds,and Flaws you can pick and choose from all of the various brief descriptions already in the Players Handbook, or try your hand at making a few in your own words. Whatever you do, work with your DM so that it all fits into the campaign world you are going to play in.
The point of this, of establishing a background, is that you enter your adventuring career as someone with a past, a past that for one reason or another led you to the adventuring life. This step in character creation helps you flesh out your role and gives you some touch points for role playing. Role playing evolves into the story of your character. As the story grows your character becomes some kind of hero in the context of the game world.
I have found that writing a brief story of "how I got here" helps me get a grip on who the character is. The background is a great starting point for beginning that "how I got here" story.
1 Tools and languages (pick a total of two) are part of the mix and match approach. Using the examples of Acolyte, Criminal, and Noble...
Acolyte: Skill Proficiencies: Insight, Religion
Languages: Two of your choice
Criminal: Skill Proficiencies: Deception, Stealth
Tool Proficiencies: One type of gaming set, thieves’ tools
Noble: Skill Proficiencies: History, Persuasion
Tool Proficiencies: One type of gaming set
Languages: One of your choice
(Source: PHB, Ch 4).