Compactions are part of the normal operation of Cassandra nodes. They run automatically in the background (otherwise known as minor compactions) and get triggered by each table's defined compaction strategy based on any combination of configured thresholds and compaction sub-properties. This video extract from the DS201 Cassandra Foundations course at the DataStax Academy talks about compactions in more detail.
It is not necessary for an operator/administrator to manually kick off compactions with nodetool compact. In fact, it is not recommended to trigger user-defined compactions (otherwise known as major compactions) because they can create problems down the track like the one I explained in this post -- https://community.datastax.com/questions/6396/.
Repairs on the other hand is something that needs to be managed by a cluster administrator. Since Cassandra has a distributed architecture, it is necessary to run repairs to keep the copies of the data consistent between replicas (Cassandra nodes).
Repairs need to be run at least once every gc_grace_seconds (configured per table). By default, GC grace is 10 days (864000 seconds) so most DB admins run a repair on each node once a week. This short video from the DS210 Cassandra Operations course provides a good overview of Cassandra repairs.
Running a partitioner range repair (with -pr flag) on a node repairs only the data that a node owns so it is necessary to run nodetool repair -pr on each node, one node at a time, until all nodes in the cluster have been repaired. This blog post by Jeremiah Jordan is a good explanation of why this is necessary.
If you're interested, datastax.com/dev has free resources for learning Cassandra. The Cassandra Fundamentals series in particular is a good place to start. It is a collection of short online tutorials where you can quickly learn the basic concepts for free. Cheers!