Although your small built-in flash works great (and if you think it doesn't join for NYC After Dark and we'll show you how great it really is!), sometimes you just need a little more control and a little bit more power. You may need to consider purchasing an external speedlight. The key difference between a built in flash unit and an external speedlite is power. A speedlite is capable of delivering up to 5-8 times more power than a built in flash. The larger the unit, the more power it will deliver. Another difference among external speedlites and a built in flash is the ability for you to articulate the direction in which the light is firing. With almost all upper end units you will have the ability to redirect the light so that you can bounce the light off of a ceiling or a wall and thus making the light softer.
Within the family of speedlight offered by each manufacturer, you will find several choices. There are some key differences between the smaller less expensive models and the larger professional models. As mentioned above - power. The smaller the unit, the less power it will deliver; so check and see what the power rating is and whether or not it's enough for you. Second, an articulating head. Smaller units do not allow you to bounce the light. Third, first and second curtain sync (or front and rear sync); smaller units do not always allow you to dictate a second (rear) curtain sync. They only do first curtain. Fourth, manual power control; professional flash units also allow you to have more control over how much power the flash delivers. Fifth, the ability to add external power. On some smaller unites you can not add an extra battery pack, thereby relying solely on the double "A" batteries. By being able to add more power to your unit means that you will be able to take several hundred photos without having to wait for it to power back up, or having to change your batteries and possibly miss a shot. The external power will also cut your recharge time to under a second; and the difference between 1 and 2 seconds is huge. Lastly, master and slave capabilities; if you plan on using more than one unit at a time to light a subject, this may be important to you. Professional units allow you to set the flash as a master or a slave; if you don't understand this, you do not need the capability. Please note that using a photo slave unit will turn any speedlight into a slave - it may be a cheaper alternative.
Should you buy from a third party? We do not recommend that you purchase from a third party; in other words, if you own a Canon camera buy a Canon flash, if you own a Nikon camera buy a Nikon flash, etc. Although it doesn't seem like it should be a problem, third party flashes are often unable to communicate with the the camera body properly. The TTL system of a branded unit also seems to work better. It is not clear why, just an observation.