How your game feels is a very important part in how your game plays. This is true for a GM running a game, and it is true for the designer who is making a game. Different systems have a different feel to them. They encourage different feels. They fit better with different kinds of stories. You don't use a system like Toon to run a super serious game, nor do you use BESM for a gritty and dangerous game. Sure, you could probably force the system into doing it for you, but that isn't what the system wants to do. Because of this, it is important to keep in mind what feel you want games to have when you are designing a system. Why and how? Well, let's discuss that.
How Capable Are the Players?
This is a choice that a game master generally gets to make, but before the GM makes the call, the designer makes it. A GM, when running a game, can choose to give players more points/levels/etc in order to run a game with more powerful people. A designer, on the other hand, actually gets to choose how powerful a player is by default. Designers for RPGs choose what the average difficulty will be in the system, how high the player will need to roll to achieve most things. They also get to decide how hard it is for a player to hit that on average.
For example, let's look at Legend of the Five Rings. In L5R the average difficulty is a 15. So, as I said above, if you want to do something that the GM considers to be of "average" difficulty for the task at hand, you need to roll a 15 or better. Now, a PC starts with a 2 in all of their stats, and a '2' in the stat is considered the average for a samurai to have. Now, 2D10 on average will give you an 11 or 12 for a result. This means that the average person needs at least 1 rank in the skill, and in fact probably 2 ranks in a skill (out of 10 total) in order to be able to reliably (Once out of every 2 tries or better).Now, what if the average difficulty was 10? Well then, that would mean that most tasks that a person ran across could be handled by a PC whether or not they had any skill in the task at hand.
Now, the GM can modify this, but the game designer sets the guidelines for how it should work, and more to the point, they set the rules for how things work against it. You can tell when a game has grown beyond the scope the designers intended for it. Things start to...fall apart in interesting ways.
How Fast Do The Players Grow?
This is also set by the designers, and is a big part of the balancing for a game. When looking through an RPG book, the game will generally give you guidelines for how much XP (or other resources used for progression) are gained by the players. The book also has the prices set for how much players have to pay to get the things they'll be wanting to get. In games with classes, they set how much stuff each class gets with the new levels, or what abilities they can get. These are all set by the designer, and when they're put in, thought is given to just how fast the game is expecting players to progress.
Believe me, there is a reason that the game book says you should give 750 XP per session, and it takes 3000 XP for a player to hit rank 2. It's because they feel that the power progression is most fun when you hit rank 2 after 4 sessions. Now, again, the GM can modify this for their game, but the guidelines are still set by the designer, and when the GM changes it they have made an active decision to change the feel of the game. Which in and of itself is important to note.
How Do The Players Compare To Other People?
This goes back to what I talked about at first, but when putting together the character rules the game designer has stats in mind for the normal person. Like I said in L5R, the average samurai has a 2 in their stat. This means that a player who starts off with a 3 in that stat, has started off better than the average person. This is one of the areas where it is harder for GMs to change how it works, because character creation often deals with characters at their most basic. Now, some game systems allow the GM to control this. GURPS for example gives players a number of points to make their characters, and the GM determines how many points that each player starts with. There is a big difference between playing in a 75 points GURPS game, and a 200 points game.
However, in most systems this base line is pre-determined. Players start off with all stats at 2, plus two stats at 3, seven skills at rank 1, and forty experience points to buy more stuff. That is a basic character for L5R, and that means that a basic character in L5R starts off with two areas where they are better than normal. This comes back into the feel for the players, because it determines how close they are to any other person on the street. The better they are than an "average" person, the more powerful the player is supposed to feel. The closer they are to those stats, the more normal they are supposed to feel.
Those are just three areas where mechanics can contribute to the feel of a game. These are also only the most basic way they do it, and how they control how powerful the player feels. There are other ways that they do this, and I'll try and talk about them at later intervals. For now though, whether you are making a game or choosing a system for your new game, take a look at the feel that your system is trying to encourage. Is that how you want it to be? If not, what would need to change to get it to how you want it?