Complicity is the legal term for assisting or helping someone commit a crime. It is more commonly known as "accessory" or "aiding and abetting." Under the law a person can be charged with complicity if they solicit, aid or abet a person in the commission of a crime. However, it does not take much to aid or abet someone. Hence the smallest little help you provide could be sufficient to establish conspiracy. Further, you might be aiding another even if you do not think that you are. For example: being the lookout for a burglary is complicity. If your roommate is growing weed in his room with a grow lamp and you split the electric bill, that could be complicity. Giving a friend a ride to his "buddies" house to buy some "supplies," that can be complicity.
I have seen many people charged with complicity who believed they did nothing wrong. The only good news, however, is that being charged with complicity and being convicted are two separate things, and often the best defense to a complicity charge is a lack of intent.