I have seen this used several times but not really sure of what it actually does. I am confused with the second grep as the argument to the first.

some commands | grep -v grep | some other commands

Can anyone provide an explanation?

Thanks,

what that command does is just filter out any text containing 'grep'. for instance if you want to look at a log file,
$> cat 'somelogfile' | grep -v grep | less
thats a pretty simple example, broken down, this is what it does, the command cat displays the contents of a file to the standard output. piping the cat 'somelogfile' to grep with the -v means to exclude anything entries thant contain the text 'grep' then piped to your pager, less, in this example. though cat is not really needed in that example, you could do it with just :
grep -v grep 'somelogfile' | less
thats the only thingi could think of right now. so really that second grep isnt a command just a string to be searched for, and in this case, filtered out.

To help with another example, it is usually used with the ps command.

For example, if you run 'ps -ef | grep sh' the output will contain all the running sh shells plus the 'grep sh' command itself. Now if you don't want to see the 'grep sh' in your ps -ef listing, you would run 'ps -ef |grep sh | grep -v grep' or 'ps -ef |grep -v grep| grep sh'. Both will have the same output, I am not sure if one will be faster then the other but if I had to guess I would say it is probably the first one because the 'grep sh' should shorten the list causing grep -v to have less to work with.

grep -v xxx simply means 'don't return xxx'. Eg if you do a
ps -ef|grep -v grep, it will return all running processes except your grep.

ps -ef |grep vold | wc -l
2


ps -ef |grep vold | grep -v grep| wc -l
1

Try:
ps -ef | grep "[v]old" | wc -l

"[v]old" is a regular expression that will match "vold" but will not match itself. This eliminates the need for that "grep -v grep" and thus will save a process.