What does 32-bit and 64-bit mean?

If you mean in terms of the processor or operating system, it refers to the number of bits which can be transferred from one place to another or processed at once. A bit is the smallest unit of data and can be either 1 or 0. 8 bits make a byte and so a byte can store 256 different numbers (the number 11111111 in binary represents 255 in decimal). Larger numbers are represented by more than one byte of data. All instructions (such as 'add these two numbers' or 'move this data to this address') are also represented by bits and bytes, so a great deal depends on how much information can be transmitted and processed in one go. Although many processors and operating systems now use 64-bit processing, much software is still written to use only 32-bit processing (in order to be compatible with 32-bit operating systems), so, in many cases, there is no real advantage in terms of speed. Over networks and the Internet, each bit is effectively transmitted one after the other in a long stream of 1's and 0's, so it doesn't matter whether a processor or operating system is 8-bit, 16-bit, 32-bit or 64-bit: the data can only get there to be processed at the same speed.

Even I don't know so I will look at this discussion. any way I think it is about colour I really have no idea.

It's the number of bits the processor can handle at once. 32-bit means 4 bytes of info per processing hit, 64-bit means 8 bytes per hit. Consequently, more is processed (and certain functions, such as mathematical things with big numbers, are easier for the processor to handle without breaking them down into smaller and smaller pieces). In practical terms, you won't notice a significant difference in two similar processors where one's 32-bit and one's 64 - unless you do a lot of serious processing.

The 32 Bit systems can process upto 4GB memory at a time. This is a very popular thing almost all the OS applications run on this. But nowadays the applications prepared require more than this so the introduction of 64 Bit took place. These things doesn't effect the system or software, these are just different versions. One 32Bit is old version and 64Bit new version.