From meta (with, sharing) + echo (have), metecho means to have a share in something, to participate in or partake of a common thing. In 1 Corinthians it becomes the key term for Eucharistic participation — eating and drinking at the Lord's Table is a real sharing in Christ's body and blood.
1 Corinthians 10:16-17 uses metecho to make a powerful argument: the cup of blessing is a sharing in Christ's blood; the bread is a sharing in his body; therefore we cannot also share at the table of demons. Participation in the Lord's Supper creates a real communion (koinonia, also v.16) — not merely symbolic remembrance but genuine spiritual participation in the benefits of Christ's death. Hebrews uses metecho for Christ himself 'partaking' of flesh and blood (2:14) — his incarnation as real sharing in our humanity.