You're completely new to Diablo?
Hmmm... well, I'm not sure where to start. The single-player and the multi-player are both played in the exact same context, the "campaign" if you want to call it this way, it has five Acts (for Diablo II and its expansion pack, Lord of Destruction), and through those Acts you'll meet with a number of NPCs in each of those Acts' main town (from which you venture on in the "wild", I guess I can put it this way). Those NPCs offer specific services such as imbuing, gambling, selling specific types of items, repairing, socketing and recruiting mercenaries (limit of one mercenary by the way).
There's a story-line, it's brief, very basic, but interesting nonetheless, it's very well told and the cinematics are still potable to watch even after all those years, they help tremendously to understand the story, because otherwise any information concerning your goals and the context of the game comes in the form of short gossip-style discussions especially with one particular NPC (whom I won't name to avoid spoilers). But the ultimate way to understand the "story" but especially the actual lore behind the Diablo universe is to read the manuals if you got them, the manual for Diablo II is especially good at telling the story of each of the character classes you can chose and the back-story of their culture and origins.
Anyway... that's about the story, but the multi-player is played within that story, with the difference being that it's on-line and you can co-operate with others, up to 7 players, to complete the game or to just play around without specifically wanting to complete any missions, because even though the game has quests each "regions" outside of the main town of each Acts are sandbox-like (although very small, understandably, it's a decade-old game), so you can just get out of the town and just hack 'n slash to gain levels and find loot. The entire game - and I do mean it - is a giant gamble, each and every single foe you kill is a "risk" and a gamble, you can invest time, healing potions, gold and item durability to kill just one monster, but you may (and believe me it will happen often) not find a single item dropping from it, and this isn't a disadvantage, it's merely a game-play mechanic, it's the principle that I'm trying to point at, there's actual "gambling" per se via NPCs where you can buy tremendously expensive but disguised items (they are simply unidentified), and once you commit your gold to buying it you will then see it being identified, which often results in a crappy item (that's gamble it its purest form), but the entire game, the rest of it, is just a brilliantly masked gamble game, everything you do is a risk, and the only direct advantage you'll ever have is to gain experience, no items drops or not, but beware that if you die in either Nightmare or Hell difficulty setting you'll lose a specific amount of experience.
In multi-player you can do Player Vs. Player, yes, and a popular type of dueling is what is called "LLD", which stands for "Low-Level Duel", up to Level 30 or so, but usually much lower than that, at around Level 10, those types of duels are considered fun since your skills are extremely basic, the items aren't granting one-hit kills powers (most of them anyway) and the dueling generally lasts a bit longer than any types of duels you'll do at high Levels with epic gear where most hits kill you immediately or reduce your health by half. I myself never liked dueling in Diablo II, I tried a lot of it back in the days, it has changed considerably since then mostly due to the new items, runewords (type of items) and skills, synergies, etc., all of which (the new stuff I mean) was introduced via patches over time (I was dueling during the 1.06 days mostly, when I started playing the game).
I know I'm forgetting a lot of things, I could write a novel about this without even noticing (which is happening right now I just know it), I've played this game too much, yet I still play it to this day (thanks to a new Ladder Season, and a new patch). If you want more information I highly recommend you to take a look at the Arreat Summit web site, but beware of certain spoilers, if you start reading the description of certain enemies or characters you may lead yourself to story-related spoilers so just try to concentrate on the basics.
Here's the direct link:
http://classic.battle.net/diablo2exp/?rhtml=y