From Diablo Wiki
Many RPGs (including Diablo II) offer skill points with each level up. Players spend these skill points to enable skills or to make already-known skills more powerful, and in those games these skill points are a core aspect of character development, customization, and play style, and they integrate into the items and other systems as well.
Diablo III had skill points through much of its early development, with these points earned every level (or every other, or ever third level). Points were awarded separately for active and passive (traits) skills, and the number of skill points and the number of points allowed in skills changed repeatedly during development.
Ultimately the skill system evolved and was simplified until points were no longer a part of it. See the skills archive article for more details about the evolution of Diablo III's skill system.
Diablo III's Skill System
Upon release, Diablo III had a much-simplified skill selection system.
Passive skills are selected from from a large menu, and these skills are either activated or not. There are no points or verying levels of strength of each passive skill. These skills can be changed at any time, as often as desired, though they have a cooldown time before they become valid, if changed while a character is not in town.
Active skills and their extensive rune effects are also selected from a menu. A character can use up to six of these skills, and they can also be changed around at any time and as often as desired. As with passive skills, there is a cooldown after changing a skill (before it becomes available) if this is done outside of town.
The skill system in Diablo III has good and bad points.
Many players like the huge variety of active skills and rune effects, and these enable a wide variety of different character builds. (Especially after the v1.0.4 patch introduced numerous skill buffs to bring unpopular skills and runes up in quality to match the most used attacks.)
The ability to respec (freespec) at will is also popular, though some fans lament the loss of a feeling of identity that having more permanent skills brought to a character. In Diablo III, there's very little rerolling of the same class, since any character can quickly change to a totally different build.
The same complaint applies to the lack of skill points, since with every skill and rune effect simply on or off, there's no building or customization to a character, as is found in most RPGs.
The skill system works in conjunction with the items system and other game features as well, so the issues must be considered holistically. For instance, items with +skill bonuses (to individual skills, to skill trees, or to all skills) were highly-valued in Diablo II. There are no such items in Diablo III since there are no skill points. A few items offer bonuses to specific skills, generally offering slightly higher damage or reduced resource cost, but these are generally small, novelty bonuses, and not much sought by players.