Information provided by T.N.Chitra
The term denotes oscillation of swaras (notes0. Carnatic music is gamaka oriented. There are two opinions on the number of gamakas (10 & 15). Some accept the no. as 10 & some 15. Some opine that the number comes to 15 due to the subdivisions within the 10 gamakas. The 10 gamakas are called Dhasavidha Gamakas.

Dhasavidha Gamakas
Aarohanam : singing the swaras in the akara brigas according to the aarohna krama of the raga.

Avarohanam : singing the swaras in the akara brigas according to the avarohana krama of the raga.
The aarohana, avarohana are generally referred to as brigas.
    AROHANA : is a series of notes in the ascending order of pitch.
    AVAROHANA : is the descending scale of notes of a raga.
Dalu : Starting from the base Shadja and basing on the raga bhava jumping to the higher notes. e.g., sm, sp, sr

Spuritham : Repeating the same swara wice. While doing so, the second time the swara is said with force. e.g., sasariri

Kampitham : Oscillating the same swara without mixing with its preceding or succeeding note.

Aahatham : Singing the swaras in the aarohana krama, giving the stress on alternate swaras.

Prathyahatham : Singing the swaras in the avarohana krama while stressing the alternate swaras.

Thripuchcham : The swara above will join the two swaras below in the same sruthi. e.g., risasa - gariri

Aandholam : Generally associated with combination of swaras which produce swinging movement. It involves jumping in a swinging manner. e.g., Sarisapapa Sarisamama Sarisagaga

Murchchana : For delineating the character of a raga the arohana, avarohana are successively delineated in a regular ascent from a swara through seven notes and a descent back to the starting note. e.g., Sarigamapadani Rigamapadanisa Nidapamagarisa

The 15 gamakas according to the other school of thought :
Thripam, Spuritham, Kampitham, Leenam, Aandholitham, Vali, Thribinnam, Kurulam, Aahatham, Ullaasitham, Plavitham, Hoompitham, Mudhritham, Naamitham, Misritham.

Learning Carnatic Music
Stages in Abhyasaganam - Swaravali, Jantai Varisai, Dhatu Varisai, Melsthayi Varisai
Stages in Abhyasaganam - Alankaram, Gitam & Swarajathis, Varnams
Tala - Structure
Tala - Angams & Jaathis
Tala - Maarga Thalams

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