You can either read through the changelog below, or check out any of the numerous update videos that Youtubers have released already. Mojang was even kind enough to post three of them on their developer blog.
Minecraft 1.5 (Redstone Update) changelog for March 13, 2013
- Added Redstone Comparator (used in Redstone logic)
- Added Hopper (collects items and moves them to containers)
- Added Dropper (similar to Dispensers, but always drops the item)
- Added Activator Rail (activates TNT Minecarts)
- Added Daylight Sensor
- Added Trapped Chest
- Added Weighed Pressure Plate
- Added Block of Redstone
- Added Nether Brick (item)
- Added Nether Quartz and ore
- Added Block of Quartz, with half blocks and chiseled variants
- New command: /scoreboard
- New command: /effect
- Containers and mobs can have custom names
- Inventory management has been changed, for example you can drag-place items over slots
- Texture packs now have separate images for each block and item, and can have animations
- Nether Quartz Ore now spawns in the Nether
- Smooth lighting now has three settings (none, minimal, maximum)
- More detailed death messages
- Some hostile mobs now are harder in Hard difficulty
- Many, many, bug fixes
- Removed Herobrine