Satellite flare (also known as satellite glint) is the phenomenon caused by the reflective surfaces on satellites (such as antennas or solar panels) reflecting sunlight directly onto the Earth below and appearing as a brief, bright "flare".

Iridium satellite flare

The Iridium communication satellites have a peculiar shape with three polished door-sized antennas, 120 degrees apart and at 40 degree angles with the main bus. The forward antenna faces the direction in which the satellite is travelling. Occasionally an antenna will reflect sunlight directly down to the Earth, creating a predictable and quickly moving illuminated spot of about 10 km diameter. To an observer this looks like an extremely bright flare in the sky with a duration of a few seconds.

Ranging up to -8 magnitude (rarely to a brilliant -9.5), some of the flares are so bright that they can be seen at daytime; but they are most impressive at night. This flashing has been some annoyance to astronomers, as the flares occasionally disturb observations and can damage sensitive equipment.

When not flaring, the satellites are often visible crossing the night sky at a typical magnitude of 6, similar to a dim star.
(definition taken from Wikipedia)

Flare produced by the Iridium-56 satellite.

Constellations near Iridium-56 flare.
In this image all constellations near the flare where drawn.
Notice the Delphinus characteristic triangles at the image top.

Detailed view of Iridium-56 flare

Flare produced by the Iridium-59 satellite.

Constellations near Iridium-59 flare.
In this image all constellations near the flare where drawn.
Notice Bootes and Corona Borealis constellations on the right side.

Detailed view of Iridium-59 flare

Flare produced by the Iridium-31 satellite.

Detailed view of Iridium-31 flare

Flare produced by the Iridium-25 satellite.