Civilization V is a much deeper, more difficult and better game than Civilization IV, here are some ways the series has improved:
Happiness is across your empire. No longer can you let your small cities wallow because unhappiness isn't affecting your big production cities. Once your empire is unhappy your production drops dramatically. If your citizens start clamouring for whales or wine or silk it's worth going out and trying to secure that resource just to make them happy.
Buildings take much longer to build. It used to be every city would have the same basic composition of buildings and some would even max out all the possible buildings you can build. Now, it's not worth it to build a granary & library & monument & temple & barracks in every single city as that would take far too long. Instead, you're forced to specialize your cities based on their surrounding terrain and position on the map with regards to your enemies.
Limited Resources: I can't stress this enough, it's so cool. Iron, horses, uranium etc. have to be secured, and not just one source either! It used to be every empire would find at least one iron, horse, oil etc, but now different deposits also have different quantities. For example I can secure an iron mine that only gives me 2 iron (hence I can only have 2 units that need iron!) or get a big one that's worth 6. This also makes city states important (since they can provide you with resources) and makes going to war over a resource a legitimate reason for warfare. This makes scouting important; if one guy is loaded with iron but no horses it'll drastically change the composition of your army. If you know that iron mine is worth 7 iron you can pre-preemptively take it out to prevent the enemy from building up his army. In Civ 4 by early mid game almost everyone has at least one mine of every crucial resource which takes away that strategic aspect.
Speaking of City States, it's EXTREMELY beneficial to accomplish missions for them. For example, 100 points for defending them from an attacker can give you (for example) +4 food in your capital and +2 food in every single on of your cities for 40 turns and +2 and +1 for 30 turns.
Technology trading: Now it costs 200 gold for each Civ to trade a random technology in 30 turns. No more bullying multiple Civs into trading techs for you, or getting an advanced tech and trading it to every single Civ for a bunch a stuff.
The Graphics: Well this is an obvious one, the graphics have been drasticly improved from the previous game, the game looks absolutely stunning in DirectX10/11 mode.
Written by RL