Remission is a partial or complete reduction in symptoms.
For example, my second attack was optic neuritis. I lost the ability to see color and my vision was blurred substantially in my left eye. 3-4 months later, after IV steroid treatments, I regained my sight in the left eye. I now have headaches and migraines on the left side but I can see normally.
That is a remission. A relapse would be a repeat of optic neuritis in the left eye.
For my transverse myelitis, my remission means a reduction in symptoms because I still have that 'plugged in' feeling in my lower body, difficulty walking, and left sided weakness. A relapse for this would mean a worsening of my symptoms.
A new attack is when you have totally new symptoms completely different than what you have already experienced. So if my right eye goes out or my right side experiences issues, I am having a new attack. (fingers crossed, candles lit that does not happen).
Lesions can heal and they can become inactive (or no longer enhance in an MRI). They can also reappear and enlarge with more damage. When an old lesion reactivates it can show up with a ring around the old damage. Lesions are a mystery since they do not totally correlate with the disability you experience. "Normal/healthy" individuals can have lesions too.
Hope this helps.
My blog: http://gothicrosie.wordpress.com/
transverse myelitis May '07 & optic neuritis Oct '07
DXd RRMS Dec. ‘07: No lesions & 3 OG bands
Hubbard MRV scan Jun. ‘10/CCSVI Jul. '10