I know that block ciphers encrypts data in the shape of specified blocks and DES also belong to block cipher family. I totally understand the procedure of DES, but I am confused that is DES take all the blocks of 64 bits of any plaint text and apply the process to all of blocks at a time or it encrypts first blocks then 2nd and 3rd and so on.. can anyone explain it Please??
This is in fact a question about modes of operation, as mentioned in a comment.
The basic operation of DES itself only defines the block cipher, and the encryption of a block. The encryption of multiple blocks with a single key is managed by the further application of a mode of operation.
Some modes of operation, like ECB, or CTR, are parallelizable. In this modes, the encryption of multiple blocks can be done independently, and so the blocks can be split apart and encrypted simultaneously.
Other modes of operation, like CBC, are sequential. In the case of CBC, each successive block requires the previous block to have been encrypted before encryption of the next block can begin.
There is a further consideration of implementation. Even a paralleizable mode, like ECB does not need to be implemented in a parallelizable way. Indeed, the simplest implementation is to continue to simply encrypt a single block at a time, so even a mode that may theoretically support encrypting multiple block simultaneously may very likely only encrypt a single block at a time in practice.
So, mode and implementation will determine how many blocks can be encrypted in parallel, not DES itself. In the real world, you're relatively unlikely to come across actual implementations that encrypt more than a single block at a time.