The Elder Scrolls V: Skyrim is the fifth installment in the Elder Scrolls series, which is a fantasy action role playing game set in an open-world. Players control their character in a first person view and explore an expansive map through open choices.
Pro Unrestrictive skill-based RPG system
Skyrim has no concept of character classes, and there are no restrictions on what equipment or magic a given character can use or learn. A character's capabilities are defined by skills (e.g. heavy armor, marksman, enchantment) which automatically improve as they are used. Levels are gained by increasing skills, and each level grants one perk -- a passive, secondary effect which further enhances a particular skill -- and increases an attribute of your choice (Magicka, Stamina or Health).
Pro The longest-running RPG-FPS franchise, with world lore rivaling classic fantasy literature
The Elder Scrolls series stretches back 20 years and has always focused on providing a rich world to explore. Skyrim inherits the stories and world-building of over half a dozen previous games.
Pro Huge variety of mods
Bethesda Softworks has upheld a tradition of releasing their internal content-creation tools to the public since Morrowind (2002). Many modders transition to new Bethesda games as they are released, bringing their experience with them and helping newcomers through forums and wikis. As a result, Skyrim's mod selection is outstanding in both variety and quality.
Pro Moral choices that can affect gameplay
Things like stealing (and getting caught), fighting or killing in towns will change how the game plays as now those people or towns will be angry with the player, which makes things much more difficult. There are also many moral choices in game such as if one should betray the person who gave then their quest by keeping the treasure they were hired to return. All of these things will change how the game plays and how NPC's react to the character making for a simulated real world of consequences.
Con Immersion can be broken due to game limitations
While the game offers players many choices some of these choices are not reflected in the game accurately. There are instances where NPCs should know who your character is or what classes they belong to but due to the limitations of the tech used in the game it is unable to "remember" these things and so NPC text will often break immersion in the game by saying the wrong things.
Con Buggy and crash prone
Skyrim, like all Bethesda in house game engines (GameBryo) is buggy and prone to crashing. Non modded games have plenty of issues, but to then add mods on top is just asking for a crash or corrupt game save.
There are still many community mods for Skyrim that try to make the game more stable by addressing memory issues and general buggynes. While the game is not as buggy as it was upon release, there are still many people that have issues with the game crashing on boot or just randomly which is why these mods are still widely used and still very relevant.