Renunciation is letting go. On a surface level it is letting go of things that are not necessary, things that we like, but that are not really necessary and often are a barrier to our practice. On a deeper level it is renunciation of selfishness, renunciation of unbeneficial qualities, renunciation of desires that are not helpful for us. With renunciation it is important to look into our lifestyle and see what desires are actually harming our growth, and through compassion we let go of some of these desires and replace them with more skillful actions.
For renunciation, we also need wisdom, as well. Wisdom guides us in our renunciation, because we have to know what desires are skillful and what desires are not, what actually blocks our development and what does not. Because at the level most of us are at, we are not going to go off to a cave and become a monk, so we have to look into our lifestyle and see what we can renounce, what we can let go of, so that our practice will be helped.
For example, if you watch a lot of TV, it could be a letting go of watching so much TV so we can meditate instead, because a lot of TV has detrimental effects on the mind. If you can't let go of all of it, then we have to see which programs are actually increasing the power of negative energies in the mind and let go of these. So it is a matter of letting go. Investigation into our lifestyles and seeing what desires cause problems for ourselves or others and letting them go.