What is a discretionary income? It's what is left over after all those bills and taxes have been paid. It includes money spent on things that are not considered essential, like holidays, luxury items and services that you could do yourself but don't want to.
Suppose you went for a week without buying lollies or chocolate, soft drinks of any kind, no renting movies or going to the cinema, no toys or magazines, don't buy lunch or coffee - how much money could you save? Why not do that for two (or more) weeks in the month and see how much you can save? Then rather than having a great big spend up stash it away in a savings account until you have enough to invest in stocks or shares. You only need $100 to start buying shares in some cases.
If you are young, you have lots of time to let that investment grow, and by the time the children have reached university age, you'll have a tidy little sum to help them further their education. If you don't need to use it for that, then you could take a great holiday, or leave it invested for your retirement. investing is really a painless way to save money.