Transparent paint is what it seems: paint that you can see through. That doesn't mean transparent paint is clear. Transparency in paint, then, doesn't necessarily mean invisible.
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Transparent vs. Translucent
Transparent paint shouldn't be confused with translucent paint. Though both let light through, translucent paint only lets you see through it partially, hiding some degree of detail and/or color.
All watercolor paint let light through so watercolor painters must paint in order of lightest (the paper) to darkest, layering see-through, but darker paints on top.
A glaze is a transparent paint made by diluting a paint or varnish, or by adding a tint to water. Thus, any paint can be made into transparent paint.
Small Particle Size
Smaller particles of pigment are more transparent because, once applied, these particles allow more of what's beneath to show through between the particles. The particles themselves are not transparent.
Less Transparency with Transparent Paint
The more transparent paint you apply to a paper, the less transparent it is because there are more pigment particles covering the paper or layer underneath.