Taken from a web search on "volcanic ash damage to aircraft engines"
Not related directly to Iceland however entirely relevent.
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Engine stall
Volcanic ash normally contains glassy materials, such as silicates, whose melting points are 600 degrees celsius to 800 degrees celsius. Since internal temperature of in-flight jet engine exceed 1000 degrees celsius, glassy particles in volcanic ash inhaled by the engines instantly melt. In the course of exhaust, the glassy materials are rapidly cooled down in the turbine chamber, stick on the turbine vanes, and disturb the flow of high-pressure combustion gases. This disorder of the flow may stop the entire engine in serious cases.
Windshield and aircraft body
Acicular solid particles in volcanic ash scratch the windshield of aircraft and lower the visiblity from the cockpit in serious cases. Ash particles also damage the paintwork of the aircraft body and corrode it.
Malfunctioning of speed meter
Volcanic ash could cause a clog-up in the pitot tube measuring air speed, and may have serious impacts on the aircraft operation.
Malfunctioning of electronic device
Volcanic ash clouds are often strongly charged, therefore may affect the wireless communication system's on the airplane.
Corrosion of the airplane body
Aerosols of hydrogen sulfide in volcanic ash cause corrosions on various components of the airplane.