What is intensified interest? It is to stick to the determined thing just as it has been determined, and the function of intensified interest is that it cannot be taken away.
It is an awareness by which one stays with what the mind [yul can] has logically established as this is so and not otherwise. Here, its specific function has been described in the words, 'it cannot be taken away', because when one has a firm conviction about the object, one is certain and cannot be swayed by anyone. For example, if one thinks about who is the infallible refuge, the Buddha or another, then one will find out that only the Buddha is the infallible refuge. Then one becomes certain, through valid means of cognition, that the teachings of the Buddha and the community which has realized the teaching are infallible refuges. Anyone who has this firm conviction cannot be swayed by any other  opinion and is counted as a Buddhist. On this basis the bright qualities of (spiritual progress) increase.
The Buddha has said that
The root of everything positive
Is the intensification of interest.
That root always matures
By producing an effect.