Followers have stats just like the player in skills and health. Those values are static and are set the first time you enter/load the zone that they are in. There are also maximum level caps for followers should your level be higher than that the first time you encounter them.
For example, most people meet Lydia very early on and she'll end up being locked in with 100 health and skills in the 20s, so she won't be as effective as Jordis (the housecarl you get in Solitude) whom you'll usually meet much later on since the house costs 25k gold to purchase.
If you are on the PC, there is a way to force an NPC to level up by resetting them:
- First, remove all the gear from the follower (at least the ones that you want to keep).
- Walk up to them, be as close as possible, open the console with the ~ key
- Click on your follower. When you do so, a string will appear at the top of your console that represents your follower's reference ID.
- On your console, type disable, then follow it up with enable
After this, your companion will be 'reset' to match what your current level is. Their health and skills should be improved.
Finally, keep in mind that all followers fall under a general category: warrior, thief, or mage. Lydia, for example, is a warrior and will never gain a sneak skill above 15 no matter what level you meet her at.