The key part of the IRI codebase here is
toProcess corresponds to the length of the
receiveQueue of the node. Transactions are added to this queue after they have been received from a neighbour and validated to be valid transactions. The receive queue stores a list of pairs of Transaction Data and Neighbour fields. Transactions in the queue are processed by being popped off it and stored in the node's database, and broadcasted to other neighbours if they are new transactions.
toBroadcast corresponds to the length of the
broadcastQueue of the node. It is the number of transactions the node is preparing to broadcast to its neighbours, either due to the above process, or because they are transactions created at this node.
toRequest corresponds to
transactionRequester.numberOfTransactionsToRequest(). The node works out how large this is by working backwards from the current milestone, and seeing how many new transactions it needs to download.
toReply corresponds to the length of the
replyQueue of the node. This is a list of pairs of Transaction hashes and Neighbour fields, and is designed to prepare transactions to send to neighbours that requested them.
totalTransactions corresponds to
TransactionViewModel.getNumberOfStoredTransactions(tangle), clearly the total number of transactions stored in the node's database.