Edit: "Each Character Level gives 5 points for Characteristics upgrades and 5 points for Support Spell upgrades (also known as specialties). Each Level will also grant additional Max HP whatever your class."
Now with the new system implemented in september each character will earn points in different branches and each one has different characteristics that you can improve acording to the lever of the character.
You still get the 5 ponts for the Support Spells but now you'll get a point according to your level in a specific characteristic (intelligence, strength, agility, chance and major).Some of these improvements have a limit, like the resistances that you can get in the intelligence branch, with a value of 10 which gives you +100 Resistances in every element. Every level the characteristic you gain a point in cycles. In addition every handful of levels you gain a point you can spend in the Major Characteristic as well as one of the other characteristics. Major Characteristic points become available at 25 and 75 and possibly at later levels.
By scrolling over each of the characteristics (intelligence, strength, agility, chance and major) you'll be able to see when you'll unlock the next point that you can spend. and if you put the mouse over each characteristic you'll be able to se if it has a limit
Also each time you level up, you'll get a speciality point that you can spend in the class specialities (spells that are specific for each class)
To sum up, each level you'll earn 5 points to spend in the specialities of your class and depending on the level you got you get a point in some characteristic.
Note: for now, one of the bests choices that you can make on the major characteristic is to get the AP and the MP. (note that you'll get a reset at lvl 30 and finally at lvl 80 if you want to try something else)