Declarations connected with relevant acts are declarations made at the time an act is occurring, about the act. In most cases, the statement will relate to an act committed by the declarant, but that is not always the case. The declaration can also relate to an act the declarant is witnessing.
Person A is at a party with a group of friends, including person B and person C. During the party person B and person C get into a heated argument and person C pulls out a gun, aims it at person B and pulls the trigger. Witnessing this, person A jumps up and yells “person C, don’t shoot!”. Person C is subsequently charged with murder. Person A is hit by a car, dies shortly before the trial and is unable to testify. This statement would be admissible as a declaration connected with relevant acts because it is a statement related to the relevant act (the shooting) that was made while the shooting was occurring, and the declarant is unavailable to testify.