What is the significance of 21 Leaves in the worship of Lord Ganesha?

Ganesha, also known as Ganapati and Vinayaka, is one of the best-known and most worshipped deities in the Hindu pantheon. His image is found throughout India, Sri Lanka and Nepal. Hindu sects worship him regardless of affiliations. Devotion to Ganesha is widely diffused and extends to Jains and Buddhists.

in the 1000 names of Lord Ganesha, ‘OM OSHADHI PATAYE NAMAHA’ is one. Means he is the owner of all medicines and their powers. That is the reason, during Ganesh Chaturthi pooja, Lord Ganesha is worshipped with 21 sacred Patras or leaves. It is believed that worshipping Lord Ganesha with his favorite leaves pleases him. A pleased Ganesha will bestow strength, long life, wisdom, wealth and prosperity upon his beloved devotees. Hence 21 Patra Puja or 21 Sacred leaves worship has become an integral part of Ganesh pooja. This is the unique worshipping for Lord Ganesha.

The 21 leaves are :

1) Shami Patra
2) Bhringraj Patra
3) Bilva Patra
4) Durva Patra
5) Ber Patra
6) Datura Patra 
7) Tulasi Patra 
8) Sem Patra 
9) Apamarga Patra 
10) Bhatakataiya Patra 
11) Sindoor Patra 
12) Tej Patra 
13) Agastya Patra 
14) Kaner Patra 
15) Kadali Patra 
16) Arka Patra 
17) Arjuna Patra 
18) Devdar Patra 
19) Marua Patra 
20) Gandari Patra 
21) Ketaki Patra

As per Ganesha Purana, Tulasi and Lord Ganesha cursed each other, Tulasi leaves are not offered to Lord Ganesha on normal days. But, as an exception, Tulasi leaves are offered to Lord Ganesha during Ganesha Chaturthi Puja which is also known as Vinayaka Chaturthi Puja.

Also, this Pooja is known to be the path to offer our body of 21 elements they are 

Pancha Gnaanendriyas: Nose (Ghruunam/smell), Tongue (Jihva/taste), Eyes (Chakshuh/sight), Skin (Twak/touch) and Ear (srothra/sound) are collectively known as Pancha Gnanendriyas or five sensory organs.

Pancha Karmendriyas: Upastha (genital organs/organs of procreation); Paayuh (excretory organs); Paada (legs); Paani (hands); and Vaak (Vaageendriya/organs of speech) are collectively known as Pancha Karmendriyas or organs of action (karma).

Panchamahaa Bhoothas: Aakaasa (sky/ether); Vaayu (air); Jala (water); Agni (tejas/fire); and Pruthvi (earth); collectively are known as Panchamahaa-Bhoothaas; the five basic elements of nature.

Pancha Praana (Vaayu): Praana (vital life force); Apaana (excretive); Vyaana (circulative); Udhaana (upward movement); Samaana (digestive) are the five vital energy forces required for the physiological functioning of the body.

and the Mind ... 5+5+5+5+1=21.

All 21 leaves are associated with 21 unique names of Lord Ganesha. Each leaf is offered while chanting a unique name Mantra of Lord Ganesha, Hence 21 Patra Pooja is also known as EKA VIMSHANTHI POOJA.