While there is no dogmatic interpretation regarding this, Catholic scholars tend to view the period as symbolic, representing an undefined period or persecution.
1,260 days is often expressed in other places in Scripture as a period of 42 months (or 3 1/2 years). This is the traditional expression used to describe the period of persecution endured by the Jews under Antiochus IV. It thus got transferred over into apocalyptic narrative to describe any period of persecution endured by the People of God.
The 1,260 days were interpreted literally by the Millerites who used this interpretation to miscalculate the Return of Christ in the late 1800s. The failure caused not only an event known as the Great Disappointment, but inspired what I, in my humble opinion, call the Great Denial–a handful of restorationist movements grew out of this by claiming that Christ did return on this date (or several years following in the early 1900s) but that this return is invisible to the naked eye.