Hello,
Yes, that directory "X" has all the graph database files which are created when you create nodes and relationships and indexes etc. Find where "X" is and compress it, Zip it, Tar it, whatever you want.
Then transfer it to the server where you are running Neo4J server. The way you do this depends on that remote server but something like using scp should work.
Once you have transferred the file decompress it and put the graph.db directory in the <neo4j_home>/data/ directory.
The names of the directories are important.
Hope that helps.