When the kohanim (priests) ascended the altar to do their work, they had to go up via a ramp, taking very modest steps. They walked placing their feet heel to toe, rather than taking large, arrogant strides (see the Mechilta on this verse). This would be absolutely impossible to do on stairs.
This mitzvah serves to reinforce the awe and reverence that one should have when approaching God and serving before Him. We should treat the Temple – and our synagogues, which serve as “miniature Temples” – with great respect. Even the stones of the altar must be treated with deference, by not exposing oneself to them. (The kohanim had trousers on under their robes and this rule still applied!)
It’s worth noting that the parsha of Yisro contains the Aseres HaDibros (the “Ten Commandments,” though there are really fourteen commandments in those ten statements) plus three additional mitzvos: not to make a human figure, not to use iron implements on the altar, and not to expose oneself while ascending the altar. These latter three mitzvos – which focus on the uniqueness of God, an abhorrence of bloodshed and the emphasis of personal modesty – correspond to the three “cardinal sins” of idolatry, murder and adultery, for which one must be willing to perish rather than violate.
This mitzvah applied to both men and women while the Temple stood. It is found in the third chapter of the tractate Middos and in the Mishneh Torah in Hilchos Beis HaBechira. It is #80 of the 365 negative mitzvos in the Rambam’s Sefer HaMitzvos.