I'm new to photography and I see the term TTL all over the place. What does it mean? And how do I use it to make my pictures better?
It means "through the lens" and generally it hooks your flash into the exposure system of the camera since the metering of the scene is through the lens. This allows the camera to exert control over the flash, including power, distance, etc. based on the scene and focal length, if the flash supports that functionality with your camera. Usually true for modern flashes made by the camera manufacturer and some third party options such as Metz.
As John says the term is usually used in reference to flash meeting. TTL meeting may improve your exposure it won't necessarily make your pictures any better! Basically the flash sends out a brief pre-flash and measures the amount of light reflected back off the subject through the lens. This is used to judge the required flash power based on your camera settings, the amount of ambient light, subject distance etc. It's helpful when you're moving around a lot and don't have time to be shooting test shots.
It can also be used with multiple off camera flash setups where you can choose the lighting ratios and have the camera work out the flash power for you. Joe McNally is a strong proponent of this way of working.
But for all it's advantages it's ultimately away of determining the correct flash power - TTL alone won't make your photos any better, learning how to use light, blending flash with ambient and most importantly bouncing flash where possible will go further toward making your photos better.
While TTL is mostly used in context of flash metering, it could also refer to basic light metering through the lens (especially in context of older cameras, when this was a luxury feature). This is how most current cameras meter their exposure. You use it to let the camera set proper exposure for scene you have currently framed, and fine-tune it by setting exposure compensation.
TTL stands for Through The Lens, and in the case of SLR metering, it indicates how the light is measured--that it's the light coming through the taking lens, rather than, say, an exterior sensor.
In flash metering terminology, a TTL system in the camera/flash combination typically means that the camera will tell the flash to send out a small "pre-flash" burst of a known brightness level, meter that flash, and then automatically adjusts the flash power to where the camera's exposure system thinks the power needs to be for good subject exposure, based upon that TTL meter reading. You can think of it like having automated exposure modes on the camera body: just as meter readings are used to automatically adjust the aperture or shutter speed depending on the shooting mode, TTL automatically adjusts the flash power output.
When speaking of a flash, a TTL flash is one that can understand the signalling protocol used to perform TTL metering, and can probably also do a lot of other "extra" features, such as high-speed sync, 2nd curtain sync, zooming, camera menu control, and possibly even has the capability of being a slave in the brand's optical-based wireless triggering system.
When talking about flash radio triggers, the TTL/manual feature distinction is similar. TTL triggers are triggers that are capable of communicating the hotshoe protocol so that features aside from syncing can be sent from the camera's hotshoe to the remote flash foot.
If you look at the flash foot or the camera hotshoe, the pin/contact that's in the center of the "square" is the sync signal. That's the signal that tells the flash when to fire so that it's in sync with the camera shutters and that the light from the flash will be used for the exposure. That is standard across all iso-compliant hotshoes, and is the only signal that's communicated with "manual" flash triggers. Features like TTL, high-speed sync, menu control, zooming, etc. etc. are all done via the non-sync pin/contact. But the electronic communication protocols for these extra features are brand-specific and proprietary. So, flashes and radio triggers that can communicate this information are more complex and typically much more expensive and possibly less robust. But you can have more features to play with.