Are you thinking of the Ptolemy Atlas World Map? That's the one major classical or medieval world make I know of that shows Europe in a fairly accurate shape but shows Italy running nearly East-to-West.
That map comes from an atlas/gazetteer written by Claudius Ptolemy in 150 AD, but not directly. The maps of the original were lost at some point in the transcription process, but the text of the book (particularly the gazetteer text, which compiled approximate latitude/longitude coordinates of a great many cities and landmarks) contained enough details to allow Medieval scribes to draft reconstructions like one I linked above. While Ptolemy's book was Classical in origin, it was widely used in the early Renaissance as one of the more reliable and comprehensive large-scale maps then available, and it was used as a basis for a number of Renaissance maps.
As for why Italy was sideways, there were few factors at work there. The first is that Italy actually is somewhat sideways: see this modern map, in a Mercator projection which distorts size enormously near the poles but depicts compass bearings accurately, and note that Italy is much closer to a NW->SE orientation than the vertical N->S orientation you had probably been remembering. And the Ptolemy map doesn't (quite) show Italy as running straight horizontal: eyeballing both maps, I'd estimate the modern one showing Italy about 40 degrees from vertical, while the Ptolemy maps shows Italy maybe 60-70 degrees from vertical. A 20-30 degree difference is still a significant error, but it's nowhere near as bad as a nearly 90-degree error would have been.
The other, I expect, is imprecision in the latitude/longitude values of the key locations anchoring the map. Most of the techniques modern cartographers rely up hadn't been developed yet: obviously there was no GPS or satellite imagery.
Beyond that there was also no trigonometric survey data: accurate large-scale surveying relies on the the theodolite, a tool combining a telescope, level, and compass to precisely measure the horizontal and vertical angles of a sight line, which could them be combined across multiple sightings to accurately calculate both distance and direction between the points in the survey. The concept of the theodolite was first developed in 1571, and was refined significantly over the course of the 1700s.
Without a theodolite, you could also use celestial observations to determine the position of key landmarks. Latitude is by far the simpler of the two, and technique was know in Ptolemy's day. The Greek scholar Eratosthenes used the basic technique as part of his data for estimating the circumference of the Earth about three centuries before Ptolemy. You just need to measure the angle of the sun at its highest point on a particular day (Eratosthenes used the summer solstice) based on the length of a shadow cast by a vertical rod, and differences in angle tell you the difference in latitude. Longitude, however, is much harder and requires an accurate timepiece that you can carry with you between the locations you're measuring. An entire post could be written about the Longitude Problem, but the short version is that all four ways of solving it (mechanical clocks that keep good time despite being rocked and jostled in transit, telescopic sightings of the relative positions of Jupiter's four largest moons, detailed calculations based on the position of the Moon relative to the fixed stars, or sending up signal rockets to broadcast the time over a wide distance) were far, far beyond Classical capabilities and wouldn't be solved satisfactorily until well into the 1700s.
That meant that while Ptolemy could compile reasonably accurate information about latitude, at least for well-known locations in the Roman and Persian worlds (note that the farther you get from the eastern Mediterranean, the worse the map gets: India in particular is nearly unrecognizable), he was largely stuck with deduction for longitude. The data available for that deduction would have come mostly from multiplying speed by travel time (particularly sea distances) or by counting paces (for land distances). That data would be a lot more available and accurate for well-traveled shipping routes, so the errors in the map are going to be concentrated outside of there: the Adriatic Sea is pretty close to the right size and shape (which is unsurprising, since it's relatively narrow and was frequently crossed by ship in that era), but the angle of the Dalmatian coast is wrong and that pulls Italy off as well.
Ptolemy was also working with an inaccurate estimate of the Earth's circumference, about a factor of 1.4x too small. This is a curious error, given that Eratosthenes had estimated the circumference correctly within a 1-2% tolerance about 300 years previously, but Ptolemy was not the only geographer of that period using the incorrect value. A modern analysis of Ptolemy's latitude and longitude values indicates that he uniformly misestimated east-west distances by the same 1.4x value, probably because he would have been reconciling angle-based measurements of north-south distances with distance-based measurements of east-west distances. And after correcting that systematic error, the analysis shows Ptolemy as much more accurate than I would have expected (about 99.3% linear correlation between Ptolemy's longitude values and modern values for the same sites) given the tools Ptolemy had to work with.
