In Exodus 3.18, they are asking to have an occasion to offer sacrifices. Ze'ev Meshel writes,
"It probably reflects the custom of pilgrimages to tombs or sacred places and mountains, a common custom among nomads."
Festivals in the ancient world often celebrated what their deity has done and seek to perpetuate deity's action on their behalf. They were usually celebrated at a holy place and therefore often required pilgrimage. In other words, it was not an established festival they were celebrating (like Passover or something like that), but instead just an opportunity to do sacrifices, celebrate YHWH, and request His actions against the Egyptians on behalf of the Israelites.
John Walton writes,
"But why could not such a feast be held in Egypt? Why is a trip into the desert necessary? Is this just a ploy to get the Israelites away from Egypt? Perhaps it is, although Moses later explains that the Israelite sacrifices would be detestable to the Egyptians (8.26).
"There may have been other more important reasons. Religious festivals are known from all around the ancient Near East. Mesopotamian and Egyptian society both had numerous feasts tied to particular times of their civil calendar. The Hittites, too, had festivals that were held monthly or yearly, while others, such as the Festival of the Sickle or the Festival of Cutting Grapes, took place in connection with events of the agricultural year (civil and agricultural calendars did not always match). In almost every case, a festival connected with a particular deity took place at the deity’s place of residence—at its temple or wherever the priests happened to place its statue. Perhaps the Israelites could not hold a festival to the god in Egypt because his place of residence was the “mountain of God” in the wilderness."