I'll be putting on my professional hat as a metallurgist for this, rather than my historian's hat. Church bells historically are bronze of some type. Bronzes are majority copper with some tin and sometimes other elements in small quantity. Without knowing the exact source for this "10,000 church bells" claim, this copper is almost certainly what the Germans would have been after. Copper is a vital military resource. You need copper in large quantities to make jackets for bullets, brass for small arms and artillery cartridges, and telegraph wire. You also need copper for a lot of background things, such as corrosion resistant pipe and catalysts for the chemical industries, or some steam engine components (remember, locomotives were hugely important for moving supplies to the front).
How much copper might you have gotten from 10,000 church bells? There is tremendous spread in bell weight, from less than one hundred pounds up to almost two tons. This is going to be sloppy math, since there are probably many more medium-sized bells than very large bells, but let's say the average weight of a bell is about 1,000 pounds. That gives us a total bell-weight of 10 million pounds. Bell bronzes tend to be fairly tin-rich, with a copper content of roughly 80 weight percent. So this means 8 million pounds of copper from these 10,000 bells. In reality you'd get less from this, as you'll have some losses from melting and refining, and older church bells tended to be even more tin rich. So skim a million pounds off of that figure - 7 million pounds of copper, or 3500 US tons.
How much of a difference would this make? I have had trouble finding a month-by-month breakdown of German copper consumption during the war, or even a breakdown of how many shells of each weight were being made, but given that Germany's prewar annual consumption of copper was on the order of a quarter million tons, the amount of copper harvested from bells alone must have been fairly insignificant to the German effort. That this was, apparently, undertaken despite the small yield is testament to how dangerous the raw material situation was for the German war effort.