Non-Political Description
“Legislatively directed spending” is a euphemism for an earmark.

Earmark is defined in plain language by the Glossary of Terms in the Federal Budget Process page for U.S. House of Representatives Committee On Rules.

Earmark - To set aside funds for a specific purpose, use, or recipient. Generally speaking, virtually every appropriation is earmarked, and so are certain revenue sources credited to trust funds. In common usage, however, the term is often applied as an epithet for funds set aside for such purposes as research projects, demonstration projects, parks, laboratories, academic grants, and contracts in particular congressional districts or states or for certain specified universities or other organizations.

Earmark is also defined in legal language in Rules of The House Of Representatives of The United States.

Rule XXI: Restrictions On Certain Bills, Section 9(d),

For the purpose of this clause, the term ”congressional earmark” means a provision or report language included primarily at the request of a Member, Delegate, Resident Commissioner, or Senator providing, authorizing or recommending a specific amount of discretionary budget authority, credit authority, or other spending authority for a contract, loan, loan guarantee, grant, loan authority, or other expenditure with or to an entity, or targeted to a specific State, locality or Congressional district, other than through a statutory or administrative formula driven or competitive award process.

Political Description
The phrase “legislatively directed spending” normally doesn’t have a political description unless it is being used to hide the fact that it is referring to an earmark.

Political Benefits
Describes earmarks while avoiding the word “earmark.”

Reference Point
Self and others who share same goal of obscuring the identity of earmarks.

Countervailing Euphemism
“Pork” or “pork-barrel project” is used to highlight an earmark in a pejorative manner.

History
From The Hill:

Because of secrecy and abuses, earmarks have become sensational symbols of excessive congressional spending. The most controversial projects are slipped into bills at conference. Lawmakers then vote on the final bill without having a clue as to what they just approved, because the earmarks were written in a secret language.

The first use of “legislatively directed spending” as an euphemism for an earmark was when House Speaker Nancy Pelosi had this to say on the House Floor as a controversy was beginning to build about the large increase in the number of earmarks that were being inserted in to bills and amendments.

If I just might direct the record to another place, why don’t we just leave this room today forgetting the word earmark? This is legislatively directed spending as opposed to executive spending.

Example Usage
Nancy Pelosi:

In the absence of legislative directed spending, you have appropriations bills that are totally dictated by the White House. And so for those who are critics of the word ‘earmark,’ understand the difference. This is a way for communities of interest in the states across our country, members to come together, sometimes in a bipartisan way, to have the Congress of the United States determine some of what is in the appropriations bills instead of just leaving it up to the White House.