A Wide Wide World
Most campaigns would give you a whole wide range of environments to explore. From forests to deserts, from wooden villages to big stone cities, you would be seeing and interacting with a lot of things on your adventure.
As mentioned previously, you would periodically do skill checks while exploring the world at the behest of the DM if you're attempting an action that involves some sort of skill.
These can be things like using Acrobatics to traverse uneven terrain or climb a tree, using Perception to detect things in the world like traps or treasures or using Stealth to hide from deadly enemies.
As you have to roll the dice for success, it is advisable to only attempt the skills you are proficient in, in other words, you have high modifiers in in order to avoid failure as much as possible as failing could result in serious consequences.
Handy Dandy!
Luckily, you're not going barehanded for this adventure as you have various tools, equipments and weapons to help you once you encouter a problem.
These can be tools such as lamps to see in the dark, potions that help alleviate diseases and injuries, armor to negate damage taken and the ever so useful weapons that can protect you from the dangers of the world. For the full list of items and equipments available, check out the Player's Handbook.
You can buy or sell these items using gold, silver and copper coins. Of course, they aren't they only thing money is good for, as you have to always have a decent sum on you in order to afford some good food and good lodging. Neccessities everybody need unless you want to be sleeping in the streets eating rats, and that would bring about a whole host of other problems.
A Deadly World
It's not all fun and games as danger lurks around every corner in this world too. Monsters and all forms of creatures alike seek to do you harm or loot your goods for their gain.
But don't fret, when that time comes, you know you're trained for this, as you draw your sword and ready your spells. You know it's time for combat.
In combat, players and enemies alike will take turns to take different actions in an attempt to defeat the other first. This is done by rolling initiatives before every battle to see who goes first and so on and so forth.
Simply put combat usually involves rolling for hit against your opponent's "Armor Class" or "AC" which is usually calculated using the armor the creature is wearing plus the creature's Dexterity attribute.
Just like DC, you have to get a number higher than your opponent's AC and you can apply your modifiers afterwards to ensure success. This usually applies to spells but some spells have special properties and rules that allows you to bypass this so it's always good to know beforehand. (Refer to Player's Handbook for full details).
If you manage to hit, you roll for damage using the die specified on the weapon or spell you're using and the opponent will lose set amount of "Hit Points"(HP). When their HP reaches 0, they die so generally combat plays in a way that you have to repeat this process until their HP reaches 0.
Do note that you also have HP of your own and your opponent will also be playing by the same rules with the DM temporily acting as the enemy so do not be careless, let the players with higher AC take the frontline or else you might be staring at death in the face.
Near Death Experience
Once your HP reaches 0 in combat, you enter an unconcious state where you can bleed out and die if you are not healed or stabalised in time.
In this state, you have to roll a saving throw whenever it's your turn where you must pass a DC of 10 with no modifiers attached. Passing it will put one strike on "Success" while failing will put one strike on "Failure". Getting three strikes on success first will let you revive yourself on the battlefield albeit severly weakened, but getting three strikes on Failure first, will unfortunately make you bleed out and your adventure would come to an end.
If the DM is lenient, he may allow your character to come back to life by introducing a revival relict of sorts for the other players to find and use. But if the DM is a little stricter, he may ask to create an entirely new character for you to enter back into the game or if we're going stricter, not even allow you to come back at all.
The Great Unknown
Well, I hope you had fun reading all this as much as I had fun writing it all. I can only hope I covered enough of the essentials or enough to ease you in for more information you may want to read up on as there is still a lot to learn of this great game.
And with that, I have nothing much else to say except I wish you good tidiings in your future adventurers, traveler. And May Your Rolls be Ever in Your Favor!