A budget is a plan that matches anticipated expenses to expected income over a specified period.
Literal
Budget [topic-とは] specified-period-during-of expenditure [object-を] anticipate-[passive-れる] income [to-に] align-[past-た] plan is-[polite-です].
Dictionary-style definition, instructive for its structure. とは ('as for [the concept of] X') is the definitional topic marker, used when introducing or defining a term — stronger and more formal than plain は. Inside the noun-modifying clause, 見込まれる ('is anticipated') modifies 支出, and the whole chain ends in 計画 ('plan'). A good example of how Japanese packs definitional content into a front-loaded relative clause.