What does Java option -Xmx stand for?

The -Xmx option changes the maximum Heap Space for the VM. java -Xmx1024m means that the VM can allocate a maximum of 1024 MB. In layman terms this means that the application can use a maximum of 1024MB of memory.

see here: Java Tool Doc, it says,

-Xmxn
Specify the maximum size, in bytes, of the memory allocation pool. This value must a multiple of 1024 greater than 2MB. Append the letter k or K to indicate kilobytes, or m or M to indicate megabytes. The default value is 64MB. The upper limit for this value will be approximately 4000m on Solaris 7 and Solaris 8 SPARC platforms and 2000m on Solaris 2.6 and x86 platforms, minus overhead amounts. Examples:

           -Xmx83886080
           -Xmx81920k
           -Xmx80m

So, in simple words, you are setting Java heap memory to a maximum of 1024 MB from the available memory, not more.

Notice there is NO SPACE between -Xmx and 1024m

It does not matter if you use uppercase or lowercase. For example: "-Xmx10G" and "-Xmx10g" do the exact same thing.

C:\java -X

    -Xmixed           mixed mode execution (default)
    -Xint             interpreted mode execution only
    -Xbootclasspath:<directories and zip/jar files separated by ;>
                      set search path for bootstrap classes and resources
    -Xbootclasspath/a:<directories and zip/jar files separated by ;>
                      append to end of bootstrap class path
    -Xbootclasspath/p:<directories and zip/jar files separated by ;>
                      prepend in front of bootstrap class path
    -Xnoclassgc       disable class garbage collection
    -Xincgc           enable incremental garbage collection
    -Xloggc:<file>    log GC status to a file with time stamps
    -Xbatch           disable background compilation
    -Xms<size>        set initial Java heap size
    -Xmx<size>        set maximum Java heap size
    -Xss<size>        set java thread stack size
    -Xprof            output cpu profiling data
    -Xfuture          enable strictest checks, anticipating future default
    -Xrs              reduce use of OS signals by Java/VM (see documentation)
    -Xcheck:jni       perform additional checks for JNI functions
    -Xshare:off       do not attempt to use shared class data
    -Xshare:auto      use shared class data if possible (default)
    -Xshare:on        require using shared class data, otherwise fail.

The -X options are non-standard and subject to change without notice.