Before I begin talking about the mechanics in the game, maybe I should give a quick primer to what an RPG actually is: RPG stands role-playing game. A RPG means you take control of a character or a group of characters. In a RPG there is a sort of development with player characters and/or some means that facilitate decision making. Lastly, there are a range of numbers or descriptors used to describe a character's strengths or weaknesses.
While RPGs can be made for computer and console games, the ones I'll be primarily speaking about are the pen and paper variety such as D&D, Pathfinder, Dungeon World, World of Darkness and so on. While you won't have the stellar graphics these video game industries can dish out there are an almost infinite amount of choices and conflicts present when you have another human hosting as the world in which your character plays in. You're not limited to following a path. There are multiple ways.
Now, just because you have a character you can play as in a world doesn't mean you suddenly can do whatever the hell you feel like doing and narrate your way to victory. Most RPGs have a means of determining success, partial success, fumbles and failures -- though not always all four at the same time. These are often handled by the random rolling of die. For example, the fabled d20 is the die used for such an occassion in Dungeons & Dragons and Pathfinder.
That being said you can always try and narrate what your character can do. This requires a bit of sportsmanship, as I said before, it all depends on the roll of the dice. Think you can take an orc army on by yourself? Well, that's where the trying part comes in. No one will stop you. There's no invisible walls laid out that force you to stay within certain boundaries. You may die doing so -- but the choice is yours. That's what, in my humble opinion, is what makes RPGs so great. You have the choice to enact how you want to handle a given situation.
Rolling the die is only part of determining success however. Characters are often proficient in certain skills used throughout the game. Take the real world for example: Chuck Norris is a pretty adept fighter, in more cases then not, he will win in fisticuffs against Stephen Hawking. However, in a showdown of intellect, more then likely Hawking would go home the prize winner. In RPGs these are generalized through the use of attributes, merits, feats, perks, abilities and a whole slew of different terminologies that showcase a characters inherent traits.
This is only barely skimming the surface of what an RPG is. There's a lot of content here. Some may be easy to understand, some may not be. Most of which depends upon the system you want to get into. Hell, I think most everyone knows all this anyway but...it helps to put down a primer.
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Thanks and game on!
Wesii