The "1117" family of ICs are low drop voltage regulators available from multiple manufacturers: e.g., LM1117 (Texas Instruments), LD1117 (ST), AMS1117 (Advanced Monolithic Systems), IRU1117 (IR), A1117 (AiT), G1117 (GMT), etc.
They come in both fixed and adjustable versions. The typical Vref is 1.25V ±0.012V. In fixed versions, the offered output voltages depend on the manufacturer: the most common ones are 1.8V, 3.3V and 5V, but there are also versions producing 1.2V, 2.5V, 3.5V, etc.
The available packages also depend on the manufacturer. The most common packages are SOT-223, and TO-220 but you'll find them in almost every common package: TO-252, DPAK, WSON, etc.
The regulator requires a minimal number of components (e.g., for fixed versions, only a 10µF capacitor connected to the OUT pin is needed for stability).
The maximum input voltage is 15V-20V, the maximum output current is 800mA-1A, and the typical dropout voltage is around 1V-1.1V at Vout=100mA and 1.05V-1.15V at Vout=500mA. For the exact specs consult your component's datasheet.
Vout = Vref (1 + R2 / R1) + R2 x Iadj (Vref = 1.25V)
Iadj is very small (around 50 µA - 150 µA), so in normal applications where the R2 value is in the range of a few kohms, the R2 x IADJ product can be omitted. The above expression then becomes:
Vout = Vref (1 + R2 / R1).
In order to have a better load regulation it is important to realize a good Kelvin connection of R1 and R2 resistors. In particular, the R1 connection must be placed very close to the OUT and ADJ pins, while the R2 ground connection must be placed as close as possible to the negative load pin. Ripple rejection can be improved by introducing a 10µF electrolytic capacitor placed in parallel to the R2 resistor.