I dealt with the same situation when I started Clomid, so I can sympathize with how confusing it can be. The month before I began my first round, they found a 5 cm cyst on my left ovary. The next month, the cyst was still there and had not shrunk or grown. The doctor let me proceed with Clomid because the cyst was stable and because it was clearly a benign, functional cyst.
I went through 2 rounds of Clomid and got bfns both times (on the second round had a light bfp on 8 dpo, but it disappeared by the next morning--I was not confident enough about it to claim it as a bfp). I was not allowed to continue with Clomid for a third round because I developed a second 5 cm cyst after my second round. The other 5 cm cyst was still there and had not changed in size. I am supposed to meet with the doctor later this month to go over my options, and I've been told that I may need to either get a laparascopy to remove the cyst or undergo another type of procedure to aspirate them.
The decision about whether you are allowed to proceed with Clomid depends on what type of cyst it is, how big it is, etc. My cyst was clearly a follicular cyst which was not growing and not big enough to really cause problems. You can still ovulate with this type of cyst so I was allowed to go ahead. It was only after the second cyst that I was told to sit out. The only thing is that sometimes if the cyst is big enough, it can affect the functioning of that ovary. The first month I was on Clomid, I did not produce any follicles in the ovary where the cyst was. The second month, that ovary produced two, but they were much smaller than the one on the right. I am convinced that the cyst was to blame for this. In my case, I needed the egg to come from my left side because that is the side of my only open tube.
So it really depends on a lot of factors.