Good posture leads to better balance. By standing up straight, your weight is centered over your feet. This helps you maintain correct form while walking and exercising. Working on posture and balance can strengthen your ability to engage in activities of daily living such as eating, cooking, bathing, dressing, housework, yardwork, castle-work, and kingdom-work.
Just walking around the house or down the block requires good balance. So does sitting down, rising from a chair, going up and down stairs, carrying packages, and even turning to look behind you.
Some of the physical reasons for poor posture include:
Inflexible muscles that decrease range of motion or the amount a joint can move in any direction. Overly tight, shortened hip muscles tug your upper body forward and throw off your center of gravity. Overly tight chest muscles pull your shoulders forward and make your look stooped over.
Muscle strength affects balance in a number of ways especially in the "core muscles" of the back, side, pelvis, and buttocks. These muscles support your upper and lower body; weak core muscles encourage slumping and loss of balance. Strong lower leg muscles keep you steady when standing.
What does good posture look like? When standing, body weight is distributed evenly on both feet, the chin is parallel to the floor, shoulders are even, the spine is straight neither flexed nor arched to overemphasize the curve in your lower back, arms are at sides with elbows relaxed and straight, abdominal muscles are tightened, and knees are even, slightly relaxed, and pointing straight ahead.
When sitting down, the chin is parallel to the floor; bilateral shoulders, hips, and knees at even heights; and your knees and feet pointing straight ahead.
You can improve your posture with a few simple exercises. Balance-specific workouts include exercises that build core strength and exercises that stretch and loosen tight muscles. Increasing core strength and flexibility can improve your posture in just a few weeks.
There are a number of free resources on the Internet which describe various exercises, among them this one for older adults. https://www.cdc.gov/physicalactivity/downloads/growing_stronger.pdf