What is interest? It is the desire to endow a desired thing with this or that particular attribute, and has the function of laying the foundation for making a start on assiduous striving.
It is an awareness which gets involved with the intended object.
The occasion, that which depends on it, and their cause and effect relationship.

 If one is unable to suppress laziness which delights in the non-inclination towards the practice of meditation and which delights in the factors not conducive to the practice, then one quickly loses all interest because first of all one does not allow the mind to go into concentration and, even if one should attain concentration, one cannot maintain its continuity. Therefore, at the very beginning it is most important to overcome laziness. When one has attained a state of alertness which is satiated happiness and pleasure both on the physical and mental level, and when one is not weary to apply himself day or night to what is positive, then laziness is overcome. In order to generate this alertness, it is important that one has the concentration which is the sustaining cause of the aforesaid state of alertness and that one makes this a continuous process. In order to have the power of concentration, one must have a strong and continuous involvement in concentration. In order that condentration be a sustaining cause factor, one must repeatedly invoke a firm conviction which enraptures one's whole mind because one has seen the virtues and value of concentration. To understand these qualities and processes in this order must be taken as the most essential point because they become clear and certain in seeing them in one's own experience.

-lam rim chen mo
The meaning of the passage, 'the occasion' in the Madhyantavibhaga, is as follows: occasion means interest, the starting point of endeavor. That which depends on it means endeavor or effort; the cause, the sustaining force of interest, means a firm conviction regarding the quality and value of the thing. The effect or outcome is alertness.

If one thinks deeply about this in the manner that Tsong-kha-pa has explained, one may discover a special importance attached to his words; however, if one has put into one's mind merely the words of the great charioteers, who state that that progress of the path follows a distinct pattern, one will gain certainty regarding practice;  but because one believes merely the words and thinks only of the arguments and supporting teachings of those great charioteers, he not only rejects the opportunity of practice, and thus loses the opportunity  of obtaining certainty about it, but he even loses the opportunity of understanding anything. Just look at how the path in which the Buddhas delight comes to life in oneself!

Interest is threefold:

1. That with which you want to meet
2. That with which you do not want to part
3. That with which you really want to get involved
There are many other involvements of interest such as the involvelment with desired things and involvement with what one sees.