Puja is prayer to The Lord. It may also be described as ritualistic worship of the Lord.
So, who is the Lord? The Lord is an All Pervading Entity, without form. To pray to that Being is difficult, because the restless mind has nowhere to come to rest, so our Seers came up with a method to help us worldly individuals to focus our minds actions and attention by giving us forms with attributes of the All Pervading.
So in Puja, we have the form of the Lord in our minds (thoughts), or physically as an idol (Moortie). We welcome the Lord, wash his feet, bathed and clothed the Lord, give The Lord ornaments etc. Having done all these actions and our minds and attention is now focused on a possible image of the formless Lord, we praise the Lord and convey our Love through the offering of flowers, fruits etc. We can also sing praises to the Lord.
More elaborately we can also offer ghee, and sweet food the Lord via the fire called Homa.
Then we wave a diya (or candle) to the All Pervading with the mental attitude that the small light (my finite self) is reaching out to the bright light (brighter than our Sun) the infinite in worship asking for a brighter intellect, peace and happiness.