Backgrounds provide a framework for character's backstory and offer dice benefits. They shape character's skills and proficiencies. In general, they contribute to character development, adding depth, personality and motivations. Backgrounds serve as a foundation for role-playing and provide plot hooks for players to utilise.
Characters that spent their youth on polishing fighting abilities, or characters that found their miliatry calling in later stage of life would definitely be interested in selecting Martial Background. Whenever it is will, duty or even raw strength that guide your character - this will be section for you.
Those that devoted themselves to a greater cause, whenever their intentions were good or of dubious nature, those that know that they have someone greater watching over them as they go forth, fulfilling their God's will - will find this section the most useful. Faith is what saves one's soul.
Does your character know how to stay invisible even in the largest crowd? Do they sweeten their words with what others want to hear in order to achieve their goal? Aren't they afraid to walk in the night, knowing that shadows aren't their enemy but an ally? Your character will likely fit Intrigue Backgrounds section, because the most terrifying sound of footsteps is the one you can't hear.
Is your character used to sleeping under gentle light of the moon? Perhaps they've spent fair amount of their life travelling, or maybe their childhood was less fortunate and they learned how to fend for themselves in not-too-noble way? Sometimes the outside can prove to be a defensive fortress, especially for characters that are not afraid of the world - this section will fit exactly those types.
Was your character living, content, fulfilling themselves in a thriving with life town? Characters that were artisans, scholars and physicians will likely find interesting choices in this section. Not everyone begins as a mastermind of a great scheme, sometimes the simplest choices are the most comfortable.