Vibrato is the oscillation of pitch. It is commonly heard in singing, string instruments, and most wind instruments. There is disagreement around the exact execution of vibrato, but it's best to emulate the greats. Below is an audio link to hear a tone with and without vibrato. Further below are video links of master musicians demonstrating a variety of vibratos.
On the right is a graphical presentation of three different speeds of vibrato. The X axis is time, and the Y axis is amplitude (pitch frequency). Depending on the context of the music, different speeds may be needed.
There is some disagreement on the physical action required to create vibrato. Some believe it is from the diaphragm while others suggest it comes from the throat. Either way, a good way to start is by practicing the exercise below. Remember to let the sound guide you--emulate the great examples of vibrato you heard in the videos above.
Set a metronome to 60 beats per minute. Google Metronome
Without the flute, say "ha" in time with the metronome, pulsing on each beat.
Now say "ha" two times per beat.
Gradually add more pulsations into each click of the metronome until you have 4 or more "ha's" in each beat
Repeat this process with your air only, and then your flute on a C in the staff.
Practice vibrato every day until it feels natural. Continue listening to master singers, string players, and flutists.
A demonstration of this exercise is below.