My bash-fu is weak; can you break that down for me?

${VARIABLE:-value} expands to the contents of $VARIABLE, if it exists, or to "value" otherwise. In this case value is ":", a bash builtin that does nothing. Effectively, the above sets PROMPT_COMMAND to run the autojump command, then to run the pre-existing PROMPT_COMMAND, if any, or a no-op.