Yes, each Mass celebrates the "Real Presence" of the body, blood, soul and divinity of Jesus Christ in the sacramental form of the consecrated bread (Holy Eucharist). However, the induction of a special "feast day" or "solemnity" had a specific purpose.
Back as early as the ninth century, there were the beginnings of disagreements started by doubters over whether or not Jesus was "really present" or just "symbolically" present in the consecrated host. In the eleventh century these arguments reached a fever pitch, until finally, one archbishop started the custom of carrying the consecrated bread in a procession. The intention was then, and still is during modern processions, to express publicly the faith of the people in the Real Presence, and to use this method to express the actual presence of the Lord among his people - specifically in the consecrated host carried tenderly in procession. In the thirteenth century the new feast day was extended to the universal church.
Today's story in Luke (Lk 9:11-17) would remind the people of Jesus' time that once again -- as in stories from Hebrew scriptures -- God was showing his love for his people by taking care of their needs (hunger) with an outpouring of great abundance. The difference between that miracle of feeding 5,000 (Luke) and today's miracle of the Mass is explained in the second reading (1 Cor 11:23-26). At the Last Supper, Jesus said "This IS my body… this IS my blood… DO THIS in memory of me…" Catholic clergy with valid ordinations have been feeding the multitudes with the Real Presence ever since, in response to this command of Jesus.
Catholics express their faith in the "Real Presence" in many more ways than a simple procession with the consecrated host. For example, we genuflect before the Tabernacle where the sacred host is reserved (I’ve actually seen some people do this with their backs to the tabernacle); or we bow reverently before the altar of sacrifice. We also worship and adore the Real Presence, by kneeling before the Tabernacle in awe and with grateful prayer for such an incredible gift from God!
Friends, be honest: what reverence do you give from your heart to the altar, the tabernacle, and the very space of the assembly?