The clear liquid would be a calcium solution and when the red liquid is dropped in, the calcium and alginate will react to produce a thin wall of gel surrounding a liquid center. This process is known as spherification.
EDIT: To make flavored beads at home follow this recipe.
Ingredients:
Raspberry mixture
3.3 oz (100 g) Apple Juice
1.3 oz (40 g) Rasberry Juice
1/2 oz (15 g) sugar
0.03 oz (1g) sodium alginate (which can be bought online or in some specialty stores)
Calcium Solution
0.08 oz (2.5 g) calcium chloride (can be bought online or in some pharmacies/specialty stores)
8 fl oz (250 g) water
Procedure
Combine raspberry mixture ingredients in a blender, blend until well combined.
Let mixture stand several hours in the refrigerator.
Dissolve calcium chloride in water.
Using a syringe (or eye-dropper, small baster, etc.) drop droplets of raspberry mixture into the calcium solution, then leave them for approx. 1 minute. The longer you leave them in the harder they will get, up until a point.
Remove beads from calcium solution and rinse in a strainer or chinois.