What is "to meet half way"

Meet \Meet\ (m[=e]t), v. t. [imp. & p. p. Met (m[e^]t); p. pr. & vb. n. Meeting.] [OE. meten, AS. m[=e]tan, fr. m[=o]t, gem[=o]t, a meeting; akin to OS. m[=o]tian to meet, Icel. m[ae]ta, Goth. gam[=o]tjan. See Moot, v. t.]

1. To join, or come in contact with; esp., to come in contact with by approach from an opposite direction; to come upon or against, front to front, as distinguished from contact by following and overtaking.

2. To come in collision with; to confront in conflict; to encounter hostilely; as, they met the enemy and defeated them; the ship met opposing winds and currents.

3. To come into the presence of without contact; to come close to; to intercept; to come within the perception, influence, or recognition of; as, to meet a train at a junction; to meet carriages or persons in the street; to meet friends at a party; sweet sounds met the ear.

   His daughter came out to meet him.
   --Judg. xi. 3

4. 4. To perceive; to come to a knowledge of; to have personal acquaintance with; to experience; to suffer; as, the eye met a horrid sight; he met his fate.

   Of vice or virtue, whether blest or curst, Which meets contempt, or which compassion first.
   --Pope.

5. To come up to; to be even with; to equal; to match; to satisfy; to ansver; as, to meet one's expectations; the supply meets the demand.

   To meet half way, literally, to go half the distance between in order to meet (one); hence, figuratively, to yield or concede half of the difference in order to effect a compromise or reconciliation with.