وَلَقَدْ نَصَرَكُمُ اللّهُ بِبَدْرٍ
And Allah has already made you victorious at Badr,
meaning, during the battle of Badr, which occurred on a Friday, the seventeenth of Ramadan, in the second year of Hijrah.
The day of Badr is known as Yawm Al-Furqan (the Day of the Clarification), by which Allah gave victory and dominance to Islam and its people and disgraced and destroyed Shirk, even though the Muslims were few. The Muslims numbered three hundred and thirteen men, with two horses and seventy camels. The rest were foot soldiers without enough supplies for the battle. The enemy army consisted of nine hundred to a thousand men, having enough shields and supplies, battle-ready horses and even various adornments.
However, Allah gave victory to His Messenger, supported His revelation, and illuminated success on the faces of the Prophet and his following.
Allah also brought disgrace to Shaytan and his army. This is why Allah reminded His believing servants and pious party of this favor,
وَلَقَدْ نَصَرَكُمُ اللّهُ بِبَدْرٍ وَأَنتُمْ أَذِلَّةٌ
And Allah has already made you victorious at Badr, when you were a weak little force,
when you were few then.
This Ayah reminds them that victory is only from Allah, not because of a large army and adequate supplies. This is why Allah said in another Ayah,
لَقَدْ نَصَرَكُمُ اللّهُ فِي مَوَاطِنَ كَثِيرَةٍ وَيَوْمَ حُنَيْنٍ إِذْ أَعْجَبَتْكُمْ كَثْرَتُكُمْ فَلَمْ تُغْنِ عَنكُمْ شَيْيًا
and on the day of Hunayn (battle) when you rejoiced at your great number, but it availed you naught... until,
وَاللّهُ غَفُورٌ رَّحِيمٌ
and Allah is Oft-Forgiving, Most Merciful (9;25-27).
Badr is an area between Makkah and Al-Madinah and is known by the well that bears its name, which in turn was so named after Badr bin An-Narayn, the person who dug the well.
فَاتَّقُواْ اللّهَ لَعَلَّكُمْ تَشْكُرُونَ
So have Taqwa of Allah that you may be grateful.
means, fulfill the obligations of His obedience