Balances
Your balance in a group is what you paid for expenses, minus your share of them, plus what you've paid back to people, minus what they've paid back to you. Positive means you're owed; negative means you owe.
Everyone's balances in a group add up to exactly $0.00, and Halvies checks this every time. Balances aren't stored: they're worked out again from the whole history, so editing or deleting an old expense puts every balance right, even after people have settled up.
With two people, the figure on the group's card is that balance, and each row shows what it did to your balance (what you paid minus your share), so the rows since you last squared up add up to the figure.
On Home, Overall is your balances in every group added together. By person shows what each person owes you across all the groups you share.