Bitcoin addresses are not pretty.  They’re between 27 and 34 characters long, and start with a “1” (they can technically start with a “3” for a “pay-to-script” address).  They look something like this:

11uEbMgunupShBVTewXjtqbBv5MndwfXhb

How did we end up with such a something so weird looking?  It’s because the Bitcoin address you have is a direct result of the cryptographic algorithms Bitcoin uses.

It all begins with the generation of an Elliptic Curve Digital Signature Address (ECDSA) “private” key.  This key is, essentially, a very long random number.  Given a private key, you can generate the corresponding  "public" key.  While you can generate a public key from a private key, you cannot generate the private key from the public key.  That’s why it’s ok to share it with the world.

The Bitcoin address you get is the result of several hashing algorithms being run on the public key (along with a few other steps like including the Bitcoin version).  So, just as you can generate the public key from the private key, you can generate the Bitcoin address from the public key.

And that’s why the addresses look so strange - they’re meant for computers to use and validate, not humans. Since each piece is mathematically related, it ensures that only the holder of the private key can claim bitcoins sent to the related Bitcoin address.

If you’d like an even more in-depth view, check out the wiki on the subject:

https://en.bitcoin.it/wiki/Technical_background_of_Bitcoin_addresses