In Roman Catholic theology, only the actual ‘act of teaching’ is properly called “infallible”. For example, according to Roman Catholic dogma, Pope Pius IX‘s teaching regarding the Immaculate Conception was infallible; it is grammatically incorrect to say “the pope is [sometimes] infallible” or to say “the Immaculate Conception is infallible”. Nonetheless, these phrases are frequently used in conversations or Catholic writings.
According to the First Vatican Council (1870-71) and as reaffirmed at Vatican II (1963-1965) the Pope is infallible when speaking ex cathedra on matters of faith and morals.
Infallibility does not refer to the inability to sin (impeccability), or to the personal holiness of a person, although it is occasionally misunderstood in that sense.