noun

• (military, also figuratively) An advance into enemy territory, an attempted invasion; an encroachment, an incursion.
  "[…] That ſince that time he [Archibald Douglas, 6th Earl of Angus] was become the ſubject of King Henry [VIII] of England, his Majeſty's [James V of Scotland's] greateſt enemy; and was now the cauſe of all the Inroads made by the English into Scotland: […]"
• (figuratively, usually in the plural) Often followed by in, into, or on: initial progress made toward accomplishing a goal or solving a problem.
  "Three weeks into it, I am finally beginning to make inroads on this project."

verb

• (intransitive, archaic) To make advances or incursions.
  "[Y]ou muſt not expect him to go with you, inroading or making incurſions into Georgia; for he is an Armenian, true to his faith; and not a Georgian, falſe and diſtruſtful!"
• (transitive, obsolete) To make an inroad into (something).
  "[Y]ea, the Saracens had lately waſted Italy, conquered Spain, inroded Aquitain, and poſſeſſed ſome iſlands in the mid-land-ſea."