Answer: In two separate Bible books written by Paul, 1Corinthians and Hebrews, he contrasts "milk" and "meat" in order to make a spiritual analogy. When addressing the Corinthian church Paul wrote the following.
And, I, brethren, was not able to speak to you as to those who are spiritual, but as to those who are carnal - even as to babes in Christ. I gave you milk to drink, and not meat; for you were not yet able to receive spiritual meat; and neither are you able now, for you are still carnal. For since envy and contention and divisions are among you, are you not carnal? . . . (1Corinthians 3:1 - 3, HBFV throughout)
The word "milk" in the above quote (Greek gala, Strong's Concordance #G1051) means the basic, elemental teachings of true Christianity first learned by new believers. The word "meat" comes from the Greek word Broma (Strong's #G1033) and means the more solid, complete and deeper spiritual doctrines of the Gospel.
Paul addressed several church-related problems in his first letter to the Corinthians. There is one problem, however, that he knew was carnal, and which was evidence of their spiritual immaturity. Some in Corinth had not only aligned themselves to certain teachers (Paul, Apollos, Peter), they were also causing contentions and divisions in the church by arguing which of these preachers was the most spiritual (verses 3 - 23)!
The apostle felt that trying to teach the church the deeper truths of God would be a waste of time so long as they continued to indulge in petty debates over who was 'the greatest!'
The same contrast between milk and meat (solid food) appears in the fifth chapter of Paul's letter addressed to the Hebrews.
Concerning Whom (Jesus and his fulfilling the role of High Priest after the order of Melchizedek) we have much to say and hard to explain, since you have become dull of in hearing.
For truly, by this time you ought to be teachers, but instead you need to have someone teach you again what are the beginning principles of the oracles of God, and have become those in need of milk, and not of solid food (Hebrews 5:11 - 12).
In verse 12 of Hebrews 5, the Greek words translated as "solid food" are stereos trophe (Strong's #G4731 and #G5160). They mean a strong or stedfast nourishment. Paul does state, a few verses later, some of the teachings he considers "milk" or are the "beginning principles of the oracles of God." They are repentance, faith in God, the meaning and purpose of baptism, the laying on of hands, the resurrection of the dead and eternal judgment (Hebrews 6:1 - 2).
In conclusion, if we use the Bible to interpret itself (which is a good, basic study rule to follow), the words meat and "solid food" refer to more advanced Christian teachings, but "milk" refers to basic Christian teachings. Interestingly, Peter uses part of this same metaphor when he writes to encourage scattered new believers.
As newborn babes, yearn after the pure spiritual milk, that by it you may grow (1Peter 2:2)