There are 2 different kinds of 'chests':
Hextech Chests: These are obtained every time you or someone in your premade group obtains an S-, S or S+ grade, while you're playing a champion with which you have not obtained a Chest yet during the season, if you have a Chest ready to drop (one per week, up to 4 charges, you can check these in your Profile from the client; these are the actual box shaped chests) these can contain:
- Champion shard
- Champion skin shard
- Ward skin shard
- Emote
- Summoner Icon
And additionally:
- Orange or Blue Essence
- Gemstone
- Hextech Chest + Hextech Key (Always together)
Champion Capsule: These are obtained every time you level up (The cilindrical shaped ones) can contain:
- Multiple champion shards
Additionally:
- Blue essence
Champion Capsules can also be Glorious Champion Capsules, which have different contents depending on the level on which these where unlocked. A Glorious capsule is obtained at every level multiple of 10 and/or 25. Here is a list of the level capsules: http://leagueoflegends.wikia.com/wiki/Experience_(summoner)#Leveling_up