This classification is based on five elements (Pancha Mahhabhuta). Though I don't have much reliable source (i.e book of Jyotisha) to cite, however, according to the book from British Library: Personal Panchanga and five source of light by Komilla Suttom, published by The Wessex Astrologer Limited, England (ISBN 9781902405261) :
The main tithi bhuta is Apas, the water element. Tithi shows our emotional stability and happiness. The water element makes this important for relationships, love and how we deal with individuals, as Venus is the primary ruler of the tithi. The strength or weakness of Venus in the natal chart would add or detract from the quality of the tithi. A tithi can also show compatibility – often people of same tithi get on well together. Each tithi also has its own bhuta ruler as well.
Five Sets of Tithis and their Sub-bhutas
There is a sub classification of tithis, which is linked to the panchamahabhuta. Tithis are divided into sets of five that repeat themselves over six times, thrice in the waxing phase and thrice in the waning. In this classification each set of three tithis are known as nanda, bhadra, jaya, rikta and poorna. Nanda tithi are 1, 6, 11 tithis; Bhadra are 2, 7, 12 tithis; Jaya are 3, 8, 13; Rikta are 4, 9, 14, and Poorna are 5, 10, 15 or 30 tithis.
Type Tithi Bhuta
Nanda 1,6,11 Agni
Bhadra 2,7,12 Prithvi
Jaya 3,8,13 Aakash
Rikta 4,9,14 Apas
Poorna 5,10,15 Vayu
The effects of Bhuta are also explained in next paragraphs, I'm here just quoting the purpose of this classification for the prediction point of view:
Apas tithi (rikta) are good at relationships but as they are rikta tithis, their inner insecurities can create problems for them. They need partners who support them as their emotional neediness is at times too much for others to manage.
Prithvi tithis (bhadra) sustain relationships. They want relationships that last.
Vayu tithis (poorna) can easily churn up their emotions. They need steadiness from relationships or else worry and stress can cause them problems.
Agni tithis (nanda) burn up relationships and are the worst offenders for selfish and short-term relationship
Aakash tithis (jaya) protects relationships.
Some blogs like this also provide similar information.
Note: answer providing references from reliable sources i.e scriptures of Jyotisha would be more useful.