The word transubstantiation is doing philosophical work. Aristotle distinguished the substance of a thing, what it fundamentally is, from its accidents, the properties by which it is perceived: colour, taste, texture, shape, chemical composition. On that scheme a thing's identity is not simply the sum of its observable properties.
The doctrine, defined at the Fourth Lateran Council in 1215 and set out at length by the Council of Trent in 1551, holds that at the words of consecration the entire substance of the bread becomes the substance of Christ's body and the entire substance of the wine his blood, while all the accidents of bread and wine remain. Nothing perceptible changes, and Catholic theology says so plainly: the change is not a matter for observation, and a chemical analysis of a consecrated host will find bread.
Two corollaries follow that outsiders often miss. First, concomitance: because the risen Christ is not divided, the whole Christ is present under either species, which is why communion in the bread alone was for centuries held to be complete. Second, the presence persists after the rite, which is why consecrated bread is reserved in a tabernacle, carried to the sick, and made the object of adoration in Benediction and Corpus Christi processions. Traditions that hold a real presence only in the act of receiving draw no such conclusion.
Trent was careful to say that transubstantiation is a fitting and proper name for the change rather than an explanation of its mechanism, which remains mystery. Later Catholic theologians, uneasy with Aristotelian physics, proposed reformulations such as transsignification and transfinalisation, describing a change in meaning and purpose. Paul VI responded in 1965 that such accounts are inadequate if offered as replacements: whatever language is used must affirm that what is there after the consecration is no longer bread.