Shields are a vital defensive tool in Dark Souls. They are particularly important for new players, giving you a much needed wall to hold against the many foes that seek to take you down. As players grow in experience and master dodging (and sometimes parrying), hiding behind a shield becomes less necessary, but they still remain useful tools, trivializing many commonplace enemy encounters throughout the game, and still serving to protect you well against quite a few dangerous boss attacks. Remember that you can swap a shield on and off your back by two handing your weapon, allowing you to use large weapons, inflict some extra damage with typical one handers, or even use dual-wield weapons in concert with a shield. With some effort, it is even possible to make use of shields as weapons, using the Shield Bash skill to smack your foes in the face.
Many shields provide either the Parry or the Weapon Skill ability. Parry grants you the ability to intercept incoming attacks and counter them, and the Weapon Skill ability let you make use of the skill of your right hand weapon while retaining your ability to block with a shield. Remember that while blocking, your Stamina regen rate is lowered, so try not to keep your shield up at all times! Block when necessary, dodge roll away from truly hard hits.
Shields are defined by their defenses, and a shield with 100% physical damage block should be one of your earliest goals as a new player. High elemental resistances are rarely necessary, but they can prove useful against certain bosses who have dangerous attacks of a specific element. Finally, the Stability value on shields is important, as it determines how well you can block extremely heavy hits. As it scales almost exactly with shield weight and size, it is generally only Greatshields that have a chance of successfully blocking the hardest blows in the game. Any shield can have its Stability value (slightly) improved by enhancing it at the Blacksmith. Infusing mundane shields with an element very slightly boosts that single elemental defense, at the cost of lowering all others. Rarely a worthwhile upgrade, again barring specific use cases against certain boss attacks.
Infusing a shield with a Blessed or Simple Gem allows you to regenerate HP or FP, even while the shield is on your back!