The statement you're referring to relates to the concept of the marginal propensity to consume (MPC) in economics. The MPC is a measure of how much consumption increases with an increase in disposable income.
When the MPC is low, it means that individuals tend to save a larger proportion of any additional income they receive rather than spend it. Conversely, when the MPC is high, individuals tend to spend a larger proportion of their additional income.
Therefore, if the MPC is low, a larger tax cut would be needed to induce a specific initial increase in consumption because people will save a lot of the money from the tax cut rather than spend it. For example, if the MPC is 0.3, then for every additional dollar of disposable income, consumption will only increase by 30 cents. This means that to achieve a specific increase in consumption (say $1 billion), a larger tax cut would be necessary compared to a scenario where the MPC is higher (say 0.8), where a smaller tax cut could achieve the same increase in consumption.
In summary, the greater the MPC, the smaller the tax cut needed to produce a specific increase in consumption, and vice versa.