Dr. Rachel Street: How Astronomers Use Color-Color Diagrams to Study Open Clusters
As we look from Earth towards a cluster, it's easy to think that we're looking through empty space. In fact, it's not as empty as all that. There can be clouds of gas and dust along the line of sight, which obscure the light from all the stars behind the cloud somewhat. The clouds tend to absorb bluer colors of light the most, causing the light from the background stars to appear more red than they otherwise would. This extinction effect is therefore called "reddening". This changes the value of the star's color indices, B-V, R-I etc.
So imagine you're looking towards a cluster. There will be other stars along the line of sight - not cluster members - both in front of and behind the cluster. And there may be clouds of dust along the line of sight as well. So the light from the cluster stars will all get the same degree of reddening. The light from any background stars behind the cluster will get reddened by the same degree at least and probably more (being further away, more dust between us and them). But the light from the foreground stars will be reddened less.
Therefore, the colors of the cluster stars will change, but they'll remain as a clump together on the color-color and color-mag diagrams, whereas non-member stars will have their colors shifted to various degrees, and they will fall in different parts of the diagram.
In this way, color-color diagrams can help us to decide which stars in our field of view are members of the cluster. But it's not a certain method because it's hard to quantify exactly how much reddening is going on (the distribution of dust in the galaxy is not uniform). If it's a field of very low reddening (little dust along the light of sight), then this technique will be less effective, and we have to resort to other methods to decide membership. The only way to decide membership for certain is to measure the motion of the stars in space over time, but this is much more demanding observationally. So color-mag and color-color diagrams are used to assign a probability that a given star is a member.