what is percentile?

Every player is recorded on the ChessWorld database in rank order, from the highest rated player to the lowest. It is common practice to consider such a ranking list in simple steps of 1% to avoid having to place many players on common levels. A player placed on the 99th percentile would therefore be a player whose current rating is above 99% of the Members. A player placed on the 50th percentile would be placed in the middle of the Membership in terms of rating. In general every percentile ranking will include a wide number of players.

For a more formal definition of the term, refer to the Percentile article available in Wiki. This page covers the mathematical context and offers relevant references for those who may be interested in exploring the concept further. 

Holy crap that's a lot of writing.

It's simple. Portion of whole divided by the whole.

In this case it's players who are worse than you divided by total number of players.

99 percentile means you're better than 99% of all players counted. In this case that means chess.com, or if looking at your national rating on a different website, then it would be among chess players in your nation.
50% means you're better than half.
20% means you're better than one fifth.
etc.

#6 - concise, clear, thx

#2 - could not finish reading that, sorry

Sorry, don't know how that happened, deleted now.

I'm  still a little in doubt about it. For instance, looking at the ccjden stats page, you see that he's #35,677 in a total of 931,409 players (as of 09/24/16).  Dividing 35,677 by 931,409 yelds 3,83% (rounded). That means his position is greater or equal than 96,17% of the players. But his percentile is 91.9%.  This leads to the conclusion that (96.17 - 91.9 =) 4.27% are in the same 91.9 percentile - (4.27% X 931,409 =) 39,771 players. Is that correct?

 Even if many people are rated the same (this link says about 20,000 have his rating) you should be able to simply divide the rank by the population to get the percentile.

So when it does the calculation, I'm guessing the number it uses for rank or the number it uses for population is different.

Lets say many people have the exact same rating. Maybe the rank on your stats page is assigned one way, and the rank used for the calculation is assigned another way (alphabetically, who had the rating first, when the account was created, etc).

For population, maybe the way inactive players are counted is different... for example just how often it's updated. Maybe 931,409 was last year's active players + new accounts since Jan 1 (for example). Or maybe 931,409 is more accurate than what they use for calculating the percentile.

#3 thank you, very informative  

So bigger the number the better you are or smaller the number the better rank you are?

The bigger the better @NukemDan

I've just played someone who didn't have a percentile but has played many games why????

Well yes the bigger number the better you are. It means you are better than "insert percentile here"

So my percentile is 98.4%, does that mean I'm better than 98% of players online?

It means that your Blitz rating is better than that of 98.4% of the players having a Blitz rating here.

What does 'percentile' mean?
If you've looked around in your stats page much, you've probably noticed a percentage number for each game type that says 'percentile.' What does that mean?

Percentile is a term used in statistics to describe the percentage of a group that falls at or below a certain level. The measure in this case, is the person's rating. In the above picture, the member is at the 42nd percentile. The percentile number here means that 42.7% of members on Chess.com have a rating that is equal to, or below this member's rating. 

For a clearer example, Hikaru's blitz percentile is 100%, because 100% of everyone on Chess.com has a blitz rating equal to, or below Hikaru's rating! 

The important thing to remember is that this number is describing the number of members who are equal to or below the person's rating. Hikaru is at 100% because no one is higher than his rating. This puts 100% of everyone at equal to, or below him. 

Another way to think of the percentile is as the percent of people on Chess.com who you are better than! 

Why can't I see my percentile? 
If your percentile isn't showing, or is showing N/A this may be because you have a new account, or because you haven't played any of that game type recently. 

In order to appear on leader-boards and have your percentile calculated, your account must be at least 7 days old.

You also must have played 20 games of that game-type within the past 90 days. If you go 90 days without playing a blitz game, for example, you will no longer be able to see your blitz percentile until you play 5 blitz games. 

You must not be muted. If your account gets muted you will temporarily be removed from leaderboards and won't be able to see your percentile, though you will return when your mute expires. 

If you are percentile 70% - it means you are top 30% of all players. 
70% of people on chess.com are worse then you in chess