Simply put, a latch is the proper attachment of the baby's mouth with your breast!
There are some things that you must know in order to latch your baby properly. First, babies do not just suck your nipple. Lil bubba must access your milk by latching onto your nipple and areola. Babies don't just suck on your breast as they would a bottle, the motion is quiet different. It's more of a compression and swallowing. Have you ever seen someone milk a cow...no seriously! They sort of kneed the breast in order to get the milk to come out. The baby is doing the same thing on your breast.
You might feel like you are stuffing your breast in the babies mouth at first. The baby will take what she needs into her mouth and start to nurse. Remember, as you and baby start to get used to nursing it will hurt less and less. When you remove your nipple from the babes mouth rule number one is "break the latch or wait for the baby to unlatch" also make sure your nipple doesn't look like the tip of a brand new lipstick. If it does, the baby is latch on improperly.
Here is the honest truth...babies are born with the instinct to nurse but they may need a little help learning and they need time to feel out your breast anatomy. If you're really lucky you and your baby will automatically hit it off the first time you put her to your breast. If you're like most moms, you and baby will need some practice. Hit up Youtube to find videos of babies latching (I've posted a link for some videos), it's one thing to see pics but another to actually see a baby doing it. You might be surprised that you and sweet angel are not too far off from the ideal latch.