The new Arduino Esplora has two orange output connectors at the top left of the device. They have been identified as for connection to Tinkerkit devices. I'm here to help the hacker use these connectors like they might on traditional Arduinos.
http://arduino.cc/en/Reference/SoftwareSerial for more information.
Programming: the pins are used as any digital pin in the Arduino software. They are digital pin 3 and digital pin 11. Both support pulse-width modulation (PWM) so you can connect LEDs, servos, etc. and vary the pulses to brighter/speedup or dim/slow down your connected device (usually done with analogWrite even though it is a digital pin). Do NOT connect a regular (non-Tinkerkit) servo directly to the pins, the pinout is different. See http://arduino.cc/en/Reference/AnalogWrite for more information. As with all connections, be careful of the power you draw.
You can power the Esplora by putting 5 volts into the Tinkerkit connectors. I highly suggest you ensure the polarity is correct several times before you actually do this as a reversed connection could destroy your device. I (carefully) do this using a LiPo battery circuit described in a previous post.
If you need more digital pins for your project than these two, you can use the ones that have been reserved for a display. See this post for more information.
Let me know what projects you build with these connectors.