In Christian culture, a quiet time is a daily observance set aside for prayer, Bible reading, and reflection. Some ministries and churches encourage their congregants to engage in regular, personal quiet times. Prayer, the reading of Scripture, and meditation on Scripture are all biblical practices. However, the Bible does not prescribe a daily time of doing all three, nor are the words "quiet time" ever used by any of the biblical writers. This is not to say that daily prayer, Scripture reading, memorization, or meditation is unbiblical. In fact, doing these things on a regular basis greatly increases one's spiritual growth and health.
The Bible depicts many of its righteous characters in prayer. It is interesting to note that the prayer lives of these men were completely different. Daniel prayed three times a day at his window, while Jesus prayed at random times of day and night, whenever He felt the need to talk to God. Paul's recorded prayers were focused on the needs of the believers, while David's recorded prayers are in the Psalms—mostly hymns and poetry extolling God's virtues or crying out to Him with personal, emotional needs. All of these ways of praying are correct.
The same dynamic can be seen in the different Bible characters' approach to the reading and study of the Word. In Psalm 119, David begs God to teach him, repeatedly outlining all the ways that Scripture is beneficial for spiritual health, growth, and understanding. Jesus is rarely shown reading the Scriptures, but He quotes the Scripture very often, showing that He had memorized large portions of it (Matthew 4:1–11). Paul uses the Word to argue and prove theological points (Romans 3:1–20), and the Word was carried directly to Daniel by the angel Gabriel (Daniel 9:20–23). And there are many other examples, throughout the Bible, of faithful characters' interaction with God and His Word. All of these are ways to spend time with the Lord and to grow closer to Him.
Quiet time should never be done out of religious obligation. If a quiet time is done at a certain time of day, or in a certain way, because someone else expects it, or because it's "the right way," it can quickly ruin joy and fellowship with the Spirit. That kind of ritualistic quiet time is to be avoided. Regular prayer and study are important and necessary to the spiritual life of the believer, but each person should find a time of day and a way of praying and studying that works for them.