The PC or player character is the 'you' in a table-top roleplaying game.
Ross is a real world person sitting at a table to play a game; he's the player. Vince Noir is a fictional adventurer that is Ross' avatar in the game; he's the character. He's sort of like Ross because he's wholly under Ross' control, Ross designed him. Obviously, Vince has skills that Ross doesn't; Vince is a master of stealth and can perform feats of magic (to my knowledge Ross sucks at magic) but more than that, Vince has a different personality to Ross. He has motivations and flaws that Ross doesn't but these are attributes that Ross thought would be fun to embody when playing the game.
PCs vs NPCs
'PC' is a handy term for ease of reference and distinguishes from non-player characters (NPCs) which are every other fictional identity the PCs can interact with in the game. The innkeeper who tells the party of a rumour of riches in the hills, the bandits who attempt to waylay them, maybe even the orcs in the caves and certainly the evil wizard at the end of the adventure. These are all identities the GM/DM may need to give a voice and personality to. I don't think the distinction ends there though. NPCs don't have any baggage, they exist only for the sake of the adventure story being played, a PC is more than that. Nobody creates a fictional character in order to save a pretend kingdom or amass unreal gold. It's entirely the other way around. The players created their characters because they wanted to play a game and often did so long before the precise adventure was decided upon. The kingdom needs saving and the gold is there to be gained to give the characters something adventurous to do so the players can enjoy a cool game and story. The entire game world and all its problems exists purely for the benefit of the players.
For the sake of completeness, it's worth pointing out that the NPCs are not the GM/DMs characters, they are mere tools. The GM/DM's character is their world and their adventure. That is what they created because they wanted to play the game and this is important too. However, I feel safe in assuming that for a decent GM/DM, their enjoyment of their creation, their game, is inherently linked to how much their players can enjoy it. I have no interest in forging onwards with a game my players aren't enjoying. To me, my players are my audience and like any fiction writer or performer, I require their approval. I'm not pretending to be selflessly virtuous, it's just that it's more of an ego trip than a power trip. I want them to love the game I run and so my adventures are designed and run for them. I don't simply need a group of people to play out my adventure, I want to create an adventure that suits them ... so that they love me for it. Yeah, I'm needy.
NPCs exist for the sake of the adventure.
The adventure exists for the sake of the PCs.
PCs exist for the sake of the players.
The PC as a single entity
Often the term PC is used to refer to the combined identities of Ross and Vince as a presence in the game. Roleplaying is when Ross makes decisions as if he were Vince, doing what Vince would do even if it's not what he, the player, would do. At the table on game night, we get to see a combined presence of Ross and Vince; the Player-Character. It's an inherent part of the fun of a TTRPG for Ross to lose himself in the identity of Vince, to become him for a few hours, either in a serious dramatic way or in a lighter, just for laughs fashion. That's what roleplaying is all about. This tends to lead us to see a PC as a single identity in our games and perhaps that is how a player should see it.
However, the GM/DM caters for both Ross and Vince separately. I think all GM/DMs do this without really thinking about it but analysing what we do and why can help us to fine tune the game experience we provide to our players. After all, they are the ones that count, the real people. If I want to run an awesome game for Ross (which is what its about for me) then I need to understand why Ross enjoys TTRPGs, who is Vince and how Ross sees him and how to marry the two. I need to create game situations that engage Ross' motivations for playing a TTRPG and motivate Vince to adventure and allow Vince to be portrayed as Ross sees him.
These aren't entirely separate things; let's imagine Ross has created Vince as a slick, wise-cracking conman, mysterious and darkly charismatic. That tells me the sort of play that Ross will enjoy and how he wants Vince to appear within the story. I can create simple social interaction challenges for Vince to overcome and this will make Vince feel smooth and confident to Ross, which is how he sees him. Vince will become more 'real' to him which is likely to make Ross lean into roleplaying Vince even more. These easy challenges don't test Ross or Vince particularly. They create an opportunities for character development and investment and can be far more effective than reveals about the plot for engaging players. These challenges might have little to do with the plot of the adventure but they are vital to creating a character and showing who he is to the other players at the table.
When the party face a gritty and dangerous section, during combats I can make sure the party's enemies are vocal, giving Ross something to bounce off with sharp retorts from Vince. I can be ready to call for suitable checks if Vince is able to goad the enemies into poor tactics. Even if the situation is desperate, Vince comes to life for Ross because there is space in the game for his character to be dry and laconic.
Our favourite books and films are often the ones with the best characters, not the cleverest plots. Run a roleplaying game, not a storytelling game.
Next in the series; Adventure Hooks and why you don't need them.