A one-shot NAND gate
Does the term "one-shot" mean anything to you? (No, it's not a nickname for some cowboy ... or a gun that holds just one bullet!)
When you finish the wiring connections, turn power ON. Press S1 once and watch what happens to LED 1.
Try holding S1 down for different periods of time ... does LED 1 stay on the same length of time or does it vary?
You see that a one-shot multivibrator has an output for a certain length of time regardless of the length of the input (it "fires one shot"!).
This means that it can be used in many circuits as a timer. You might also see this circuit called a monostable multivibrator. Since this is a multivibrator, you might suspect that there's some way to vary the time it produces an output.
You're right - there is a way - and we'll let you try to discover what it is. (Actually, you shouldn't have much trouble discovering which parts you need to change. Be sure to make notes about the effect of higher and lower values on circuit operation.)