Proposed legislation is subject to an analysis that estimates its effect on the budget deficit. Under static scoring, the legislation itself is not assumed to change the economy. Thus, for example, if a 1% drop in tax rates is proposed, the effect on the deficit can be easily computed by reducing anticipated tax revenues from that tax by 1%.
Dynamic scoring recognizes that the change in taxes will further influence taxpayer behavior, which will further affect revenues received (separate and apart from the change in rate itself). In the above example, it would say that the drop in revenue will actually be less than 1%, because taxpayers would be encouraged to participate more in the taxed activity, thus increasing overall amounts subject to the tax. Alternatively, a tax hike of 1% would not bring in 1% additional revenue, but something less because taxpayers would now be disincentived from participating in the taxed activity, so less tax revenues from it will arise than if the tax was unchanged.
This is probably more intellectually honest than static scoring. But since it involves estimates, it has a greater chance of error and/or manipulation. Given that the budget estimates themselves tend to be far off from reality anyway, with or without dynamic scoring, perhaps the intellectually honest approach is the best approach. The politics are that those who want to cut taxes generally favor dynamic scoring, while those who oppose tax cuts prefer static scoring. The politics are more muddied when looking at the question of whether or how much to raise taxes.
The House of Representatives this week adopted dynamic scoring, but only as to big ticket legislation.