When the blood of two people is mixed together, it clumps or forms visible chunks in the liquid plasma. The red blood cells become sticky and clump together.
This is what agglutination looks like
This is also how an Eldon Card for testing blood type will look when typing your blood. The Agglutinated circle shows you what blood type you are.
Here are a couple model pictures to show how agglutination occurs between antibodies and antigens on the surface of our red blood cells (RBC’s)