what does -zxvf mean in tar -zxvf <filename>?

Instead of wading through the description of all the options, you can jump to 3.4.3 Short Options Cross Reference under the info tar command.

x means --extract. v means --verbose. f means --file. z means --gzip. You can combine one-letter arguments together, and f takes an argument, the filename. There is something you have to watch out for:

Short options' letters may be clumped together, but you are not required to do this (as compared to old options; see below). When short options are clumped as a set, use one (single) dash for them all, e.g., ''tar' -cvf'. Only the last option in such a set is allowed to have an argument(1).

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This old way of writing 'tar' options can surprise even experienced users. For example, the two commands:

 tar cfz archive.tar.gz file
 tar -cfz archive.tar.gz file

are quite different. The first example uses 'archive.tar.gz' as the value for option 'f' and recognizes the option 'z'. The second example, however, uses 'z' as the value for option 'f' -- probably not what was intended.

• z means (un)z̲ip.
• x means ex̲tract files from the archive.
• v means print the filenames v̲erbosely.
• f means the following argument is a f̱ilename.

For more details, see tar's man page.