What does Grace At Meals mean in the Bible?

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Charles Buck Theological Dictionary - Grace at Meals
A short prayer, imploring the divine blessing on our food, and expressive of gratitude to God for supplying our necessities. The propriety of this act is evident from the divine command, 1 Thessalonians 5:18 . 1 Corinthians 10:31 . 1 Timothy 4:5 . From the conduct of Christ, Mark 8:6-7 . From reason itself; not to mention that it is a custom practised by most nations, and even not neglected by heathen themselves. The English, however, seem to be very deficient in this duty. As to the manner in which it ought to be performed, as Dr. Watts observes, we ought to have a due regard to the occasion, and the persons present; the neglect of which hath been attended with indecencies and indiscretions. Some have used themselves to mutter a few words with so low a voice, as though by some secret charm they were to consecrate the food alone, and there was no need of the rest to join with them in the petitions. Others have broke out into so violent a sound, as though they were bound to make a thousand people hear them.
Some perform this part of worship with so slight and familiar an air, as though they had no sense of the great God to whom they speak: others have put on an unnatural solemnity, and changed their natural voice into so different and awkward a tone, not without some distortions of countenance, that have tempted strangers to ridicule. It is the custom of some to hurry over a single sentence or two, and they have done, before half the company are prepared to lift up a thought to heaven. And some have been just heard to bespeak a blessing on the church and the king, but seem to have forgot they were asking God to bless their food, or giving thanks for the food they have received. Others, again, make a long prayer, and, among a multitude of other petitions, do not utter one that relates to the table before them. The general rules of prudence, together with a due observation of the custom of the place where we live, would correct all these disorders, and teach us that a few sentences suited to the occasion, spoken with an audible and proper voice, are sufficient for this purpose, especially is any strangers are present. Watts's Works. oct. edit. vol. 4: p. 160. Law's Serious Call, p. 60.
Seed's Post. Ser. p. 174.

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Blessing (2) - ...
The Biblical command on which the obligation of Grace at Meals (Heb
Old Testament (ii. Christ as Student And Interpreter of). - the keeping of the Sabbath, fasting on the Day of Atonement, the simpler forms of prayer, and Grace at Meals