Praise be to Allah.
The sun and moon are two of the signs of Allaah. By means of lunar and solar eclipses, Allaah reminds His slaves of the Day of Resurrection, the Day on which their light will disappear. Allaah says (interpretation of the meaning):
“So, when the sight shall be dazed.
8. And the moon will be eclipsed.
9. And the sun and moon will be joined together (by going one into the other or folded up or deprived of their light)”
So by means of this sign Allaah reminds us of that Day. See also question no. 5901. And the Prophet (peace and blessings of Allaah be upon him) hastened to pray when that happened.
When you saw the eclipse when you were going out for Fajr prayer, you had the choice of starting with the eclipse prayer, as suggested by some scholars, because of the command narrated from the Prophet (peace and blessings of Allaah be upon him) to hasten to do that. But if you started with Fajr first, this is also good because the obligatory prayer should come first. This may also serve an interest, especially since the eclipse could not be seen except at the time of the iqaamah, so it may have been too difficult for the people, especially those who had stayed up at night during the blessed month, if the imam had started with the eclipse prayer. So he started with Fajr prayer, to enable those who wanted to leave to do so, as that would be easier for the people; this is also less likely to cause confusion, especially for those who had come for Fajr and did not know that the imam was going to offer the eclipse prayer.