Monstrance at the monastery of Bidaurreta, Spain (public domain/source: Wikimedia Commons)
The Catechism of the Catholic Church defines contemplation like this:
A form of wordless prayer in which mind and heart focus on God's greatness and goodness in affective, loving adoration; to look on Jesus and the mysteries of his life with faith and love.
I emphasized "wordless prayer" because that is often what people struggle with the most. Critics of contemplation attack it because they see it as "emptying the mind" which they think makes it too similar to eastern meditation (which is an erroneous idea - eastern meditation is actually about mindful awareness more so than emptiness, whereas self-emptying or kenosis is very much a Christ-like act), or worse, that it leaves us vulnerable to demonic attack (also erroneous: from the desert fathers and mothers on, the Catholic tradition has always maintained that temptation comes to us through our thoughts, not through silence!).
But for many people, the problem with wordless prayer is much more prosaic: we struggle with it because as soon as we enter into silence, we encounter an endless array of inner distractions: images, ideas, feelings, thoughts. How can we enter into wordless prayer when our minds and hearts are, well, so wordy?
Here's one way that Catholics (or any Christians comfortable with Eucharistic adoration) might approach this question. Our conscious awareness is continually bombarded with thoughts, ideas, imaginations, daydreams, etc. But silence is always present, within and between all of our thoughts. So why not think of silence as that always-present place within us where we "focus on God's greatness and goodness in affective, loving adoration" - and our thoughts and other distractions function as the "container" in which our silence is held?
In other words: thoughts are to contemplative silence like a monstrance is to the Host!
Thoughts are like a monstrance. Silence is like the host. All our thoughts contain silence within them, and the silence contains the presence of God. When we seek to be present to God in silent prayer, we need not be troubled by our thoughts. We can appreciate them, the same way we appreciate a beautiful monstrance. However, the point is not to be distracted by the monstrance, but to keep returning our attention to the host in the center. Likewise, in prayer, let us not be distracted by our random thoughts, but keep returning to the silence at the center of every thought, for it is in the silence where we meet the wordless loving presence of God.