In plain words
To wear new clothes with inner purity as the aim: that is its meaning. All these have been teaching inner meanings and spreading the spiritual principle.
By purity of Manas both Buddhi and Siddhi are attained
On this Gaṇapati day we perform many kinds of worship and offer kuḍumulu and uṇḍrāḷḷu to God as naivedya. What kind of things should we offer God as naivedya? They should be things cooked only by steam, without the touch of oil and without going into the fire. That is why people set rice flour in steam like idli, put a little sesame flour or green gram in it, and call it ‘uṇḍrāḷḷu’. Neither fire nor oil touches them at all. What is its inner meaning? In the month of Bhādrapada, by this Caturthī day, the sesame crop reaches the farmers' homes. This sesame flour is a divine medicine for ailments of the breath and ailments of the eye. When we put it into rice flour cooked in steam and cook it, that food digests very easily. So, keeping both these in view, health and Ānanda, the ancients made their offering to Him in this way when they worshipped Vināyaka. Only when Manas is pure does Buddhi blossom. Only when this Buddhi blossoms does Siddhi come to it. So by purity of Manas both Buddhi and Siddhi are attained. Vināyaka weds this Buddhi and Siddhi. What does ‘Siddhi’ mean? The attainment of Jñāna alone is the true Siddhi. Purity of mind alone is the true Siddhi. So to Siddhi and Buddhi are born sons named Kṣema and Ānanda. The śāstra has taught that Kṣema and Ānanda are both sons of Vighneśvara, and that Buddhi and Siddhi are both Vināyaka's consorts. As for who the consorts are: the power of attraction. For example, we set out some metals: iron, silver, brass, gold and so on. If you place a magnet among them, it draws only the iron; it does not draw the gold for being precious. In the same way, since Gaṇapati is joined with Siddhi and Buddhi, He draws only the pure heart.