SegWit, specified in BIP 141, replaced the old one-megabyte size limit with a weight limit. Weight counts each byte of a transaction's non-witness data as four units and each byte of its witness data, mostly signatures, as one. A block may weigh at most 4,000,000 units.
The virtual byte is weight divided by four, rounded up. It lets fees be quoted per byte as they were before SegWit: a transaction without witness data has the same virtual size as serialized size, and one with witness data has a smaller one. Bitcoin Core's relay policy can count a transaction as larger than its weight implies when it carries an unusually high number of signature operations.
The Network tab sizes the queue in virtual bytes, so its count of full blocks waiting is a count of whole millions of vbytes.