Let's look at this with the help of an example. Suppose we have a direct mapped cache and the write back policy is used. So we have a valid bit, a dirty bit, a tag and a data field in a cache line. Suppose we have an operation : write A ( where A is mapped to the first line of the cache).
What happens is that the data(A) from the processor gets written to the first line of the cache. The valid bit and tag bits are set. The dirty bit is set to 1.
Dirty bit simply indicates was the cache line ever written since it was last brought into the cache!
Now suppose another operation is performed : read E(where E is also mapped to the first cache line)
Since we have direct mapped cache, the first line can simply be replaced by the E block which will be brought from memory. But since the block last written into the line (block A) is not yet written into the memory(indicated by the dirty bit), so the cache controller will first issue a write back to the memory to transfer the block A to memory, then it will replace the line with block E by issuing a read operation to the memory. dirty bit is now set to 0.
So write back policy doesnot guarantee that the block will be the same in memory and its associated cache line. However whenever the line is about to be replaced, a write back is performed at first.
A write through policy is just the opposite. According to this, the memory will always have a up-to-date data. That is, if the cache block is written, the memory will also be written accordingly. (no use of dirty bits)