Skills are special powers that characters can learn in their adventures. You recieve 1 skill point every time you level. Skills are spent in a tree unique to your class.
Below level 30 you can redistribute your skill points as you will. After level 30 you need to buy Redistribution Points. It says you need to pay Dragon Gold for them, but once you get into the payment dialogs it gives you the option of paying with Dragon Stones instead.
The skills delivered seem to be dependent upon both your level with the skill (you have a level with each skill from 0 to 9, each change costing 1 skill point) and your charcaters level. Spending points on a skill when you don't have a high enough character level is wasteful.
The number of skill points you get is such that you will not be able to fully populate the skill tree (at least at lower levels). Consider specializing in a subset of the skills rather than being mediocre at everything. This is especially true of mages - lightening or fire, not both.