I am DMing a campaign. The party was fighting two castle guards, and killed one of them. The other guard attacked them, got past the AC of one of my players. He said he could dodge, but I don't know if you can or not.
Can you roll to dodge a attack? Or can you dodge at all?
I thought your AC already represented your agility (to dodge) and armor.
In D&D 5E, a player cannot roll to actively dodge an attack. This happens in such systems as Warhammer Fantasy, Dark Heresy and potentially a lot of other RPG systems. But not D&D 5E.
In D&D 5E the dodge action can only be taken on your own turn as per page 192 of the Player's Handbook described under the (aptly named) Dodge action:
When you take the Dodge action, you focus entirely on avoiding attacks. Until the start of your next turn, any attack roll made against you has disadvantage if you can see the attacker, and you make Dexterity saving throws with advantage. You lose this benefit if you are incapacitated or if your speed drops to 0.
You have to call and dedicate one full action during your turn to actively dodging any and all attacks coming your way until the start of your next turn. But even taking this action, a player would not make a "dodge roll" to dodge the attack.
Caveat
The rules as written do not give any character the means to intervene without specific abilities given by racial/class features, feats, spells/magic items, homebrew rules.
An example a such a feature enabling a player to interrupt an opponent's turn to protect themselves is a spellcaster using the level 1 spell called Shield. With a reaction action they could give themselves a +5 bonus to AC until the start of their next turn.
The D&D combat system assumes that you are running around, jumping pit traps, casting spells, and hitting people all while trying not to be hit yourself. The Dexterity component to AC already includes normal attempts at not being hit by expedient of being somewhere else.
From PHB page 14:
Your Armor Class (AC) represents how well your character avoids being wounded in battle. Things that contribute to your AC include the armor you wear, the shield you carry, and your Dexterity modifier.
And it further clarifies that
Without armor or a shield, your character's AC equals 10 + his or her Dexterity modifier.
That is, you don't need any armor at all to have an Armor Class. Also note that the Dexterity modifier can be limited by the armor you wear. This is a way of expressing that physically dodging is more difficult with heavier armor, and contributes to the idea that you are doing this all the time by default.
It is possible to spend some extra focus in combat on trying even harder to move out of the way. This is known as the Dodge action. There are two notable issues.
First, you need to take this action before you expect to get hit a lot.
Second, this takes an Action, so you aren't doing things like stabbing the bad guy.
The Basic Rules defines Hit Points like this, on page 77:
Hit points represent a combination of physical and mental durability, the will to live, and luck. Creatures with more hit points are more difficult to kill. Those with fewer hit points are more fragile.
It expands on this with an aside at the top of the next page:
Describing the Effects of Damage Dungeon Masters describe hit point loss in different ways. When your current hit point total is half or more of your hit point maximum, you typically show no signs of injury. When you drop below half your hit point maximum, you show signs of wear, such as cuts and bruises. An attack that reduces you to 0 hit points strikes you directly, leaving a bleeding injury or other trauma, or it simply knocks you unconscious.
A successful attack isn't a sword actually slicing flesh. Combat experts are going to know how to avoid being hurt, but doing so takes effort which is in limited supply. Like Westley wearing out Inigo in The Princess Bride. There is no doubt that they both had successful attack rolls throughout the duel.
In this same way, your player's character successfully dodged the enemy's attack, but it took considerable effort to do so. That effort is reflected in a loss of HP. Clean and/or easy dodges that don't take effort are reflected in the character's AC, in the form of a Dexterity Bonus.
I recommend addressing these concerns via narration. Describe the way the character dodged or deflected the attack by the skin of their teeth, maybe leaving a slight cut on an arm or leg, when the attack hits them. And when the attack misses, describe how the character sees the attack coming and deftly steps aside. This has served me well with my tables of new players, who are more used to seeing their Skyrim character with arrows sticking out of them and are concerned about the long-term effects of taking damage. Eventually they'll become better adjusted to the mechanics and will no longer need such descriptions.
