What are astroparticles?
Astroparticles are particles that have an astronomical origin.
Let's work through a definition this way:
First off, a particle is a very small bit of something that has mass and/or radiation. Particle physics studies them - most especially the ones that are the smallest detectable particles, and the forces and fields that influence them.
Astroparticles are particles that have an astronomical origin and the study, astroparticle physics looks at how astroparticles relate to astrophysics and cosmology.
The astroparticle wiki link can take you to an article that discusses astroparticle physics - the questions they are working on, the methods they use, and the like.