Close the terminal but keep matlab running remotely

In Unix-type systems using the most common command shells, a command line "<" followed by a path indicates the source of standard input (stdin). A command line ">" followed by a path indicates the destination of standard output (file id 1, stdout). A command line "2>" followed by a path indicates the destination of the error stream (file id 2, stderr). The path /dev/null on input is the completely empty file, so "< /dev/null" mean that there is no input. The path /dev/null on output means that the corresponding output is to be thrown away. Thus "< /dev/null > /dev/null 2> /dev/null" means that the program is get end-of-file immediately if it ever tries to use input, and anything it outputs on the standard output or standard error streams are to be thrown away.

If these parts of the command line were not provided, then when you used nohup, if the program ever needed input it would try to read from the terminal you issued the nohup command on; that would generate confusion at the very least, and probably an error (instead of a clean "there is no more input"). Likewise if the program ever needed to output then without those parts of the command line it would try to write to the terminal you started the nohup on, leading again to confusion or an error.

Note: I missed a character in the command. You should use

nohup matlab -nosplash -nodesktop -r "try; script; catch; end" < /dev/null > /dev/null 2> /dev/null &

Notice the "&" at the end of the line. That tells Unix-like systems to run as a separate process instead of waiting until the command finishes before allowing you to enter further commands.