I selected tourism as the purpose when I applied for my visa and was given a 2-year multi-entry C visit visa. I have a business trip next month; can I use this visa to enter the UK for business?
Yes, you can mix and match the purpose of each visit. Business, leisure, academia, medical and so on within the rules are all fine.
The controlling reference point for your question is Appendix 3, Permitted Activities for All Visitors, of Appendix V of the Immigration Rules.
All visitors are permitted to undertake the activities listed in paragraphs 3 – 27 of this Appendix provided they meet the requirements at V 4.5- V 4.8.
If you find your proposed activity in Appendix 3, then it is covered by the Standard Visitor Visa (or any other class "C" UK visa). As always, bring the evidence you used to apply for your visa with you for possible inspection by the IO who lands you.
In comments you expressed anxiety about the explaining the purpose of your visit and how it corresponds to the application you made. To cope, you should print out a copy of Appendix 3 and highlight the permitted activities that correspond to your agenda in the UK. Carry your print-out with you in your hand luggage.
Regardless of what you wrote down on your application, the Entry Clearance Officer approved you for everything on the permitted activities list. It's how the Standard Visitor Visa works.