"Swingy" is just a term used to describe combats where randomness plays a greater role than some might like. Its contrast is probably "grind." The only real difference is probably the number of die rolls needed to resolve complex questions of game resolution. If you think of combat in an RPG as a random walk between two extremes of "win" or "lose," the only difference is how many steps it takes to get to the end of the walk. The swingy game only takes a few steps, and each step can move you dramatically across the scale. The grindy game takes a longer walk, and each step contributes less.
The advantage of the swingy game is that there's a sense of risk all the way up until the last moment. The advantage of the grindy game is that there's less of a chance that randomness will render your strategic work moot. The disadvantage of a swingy game is that you can do everything right and then lose anyway because the die fell in a particular fashion. The disadvantage of the grindy game is that you can do everything right and ensure the inevitability of victory several rounds in advance of its arrival.
Examples:
Swingy: 3e- Combat with an enemy spellcaster. You roll initiative, and either win or lose. If you win, you hit him with a save or die spell that could kill him instantly, or you charge him with a fighter geared up to do more damage in a single round than he has in hit points. If he wins, he does the same thing to you.
3e- Your Paladin has been trading blows with the enemy Blackguard for several rounds. You were ahead, until he rolled a critical hit with a smite good attempt using a greataxe that's had its critical hit bonuses magically enhanced, and you took more damage than you originally had in hit points.
Grindy
4e- You're in a fight with a group of monsters who rely on a particular tactic to deal their damage- they have two lightly armored, low hit point monsters who deal a lot of damage with ranged spells, and two heavily armored, high hit point monsters who deal low damage but protect the spellcasters. You've figured this out, and used your tactics and your powers to slip past and kill the spellcasters. Now you've just got these two guardian monsters to kill. Their damage is laughably low as a group without their key members, and you'll win eventually, but its going to take time.
The advantage of the swingy game is that there's a sense of risk all the way up until the last moment. The advantage of the grindy game is that there's less of a chance that randomness will render your strategic work moot. The disadvantage of a swingy game is that you can do everything right and then lose anyway because the die fell in a particular fashion. The disadvantage of the grindy game is that you can do everything right and ensure the inevitability of victory several rounds in advance of its arrival.
Examples:
Swingy: 3e- Combat with an enemy spellcaster. You roll initiative, and either win or lose. If you win, you hit him with a save or die spell that could kill him instantly, or you charge him with a fighter geared up to do more damage in a single round than he has in hit points. If he wins, he does the same thing to you.
3e- Your Paladin has been trading blows with the enemy Blackguard for several rounds. You were ahead, until he rolled a critical hit with a smite good attempt using a greataxe that's had its critical hit bonuses magically enhanced, and you took more damage than you originally had in hit points.
Grindy
4e- You're in a fight with a group of monsters who rely on a particular tactic to deal their damage- they have two lightly armored, low hit point monsters who deal a lot of damage with ranged spells, and two heavily armored, high hit point monsters who deal low damage but protect the spellcasters. You've figured this out, and used your tactics and your powers to slip past and kill the spellcasters. Now you've just got these two guardian monsters to kill. Their damage is laughably low as a group without their key members, and you'll win eventually, but its going to take time.