One can spend money on (invest in) things that provide only immediate benefits, or in things that provide continuing benefits into the future.
How do the above statements relate to the accounting equation?
Well, the elements on the right side show where money comes from. These are the sources of finance. Equity and liabilities are external sources of finance. Income is the business itself creating finance for more assets.
The two items that increase on the left side show what has been invested in. One can invest in items that provide immediate benefits only (expenses) or continuing benefits(assets).
The water bill for January (for example) is an expense as the benefits for that month have been immediately consumed and there will be no more benefits arising from the January water bill in future (the water bill for February is a separate expense that will be paid later and that will provide benefits specifically for February).
In contrast to this, a construction vehicle purchased in January is an asset as it will provide benefits for the business well beyond January.