Clicking on an item shows a bunch of information about the item, plus controls you can use to move the item, compare it with other items, and add tags or notes. Click on the name of the item to bring up the Armory page which gives even more details about the item.
Perks and Mods
Hover your mouse over, or press your finger on, a perk or mod to see what its effect is. One thing that may be counterintuitive is that you may see different bonuses from perks or mods depending on which item they're on. This isn't a bug - it's how stats work in Destiny. See this article for more info.
You can click on different perks to preview what their stat effect would be. Click "Apply Perks" to save the perk selections to your item.