It's the state of the encryption. The pending state includes new encryption keys, and initialization vectors. There is a write key for sending data, and a read key for receiving data. The state of the keys and resulting IVs are the read and write states.
So when the current read/write state is overwritten with the pending read/write state it means that the new encryption keys and IVs are to be used for future communication. Until a new Change Cipher Spec message is received.
The significance of these states is that they keep track of the cryptographic state as data is being encrypted and decrypted. When a new key is negotiated these states are updated to use the new key that was negotiated between the peers. Key renegotiation is common among most cryptographic protocols.
To follow up on the comment by @Makif, the cryptographic state is complex. It keeps track of:
- Symmetric algorithm (mode of operation and size)
- Asymmetric algorithm
- Symmetric encryption keys
- Initialization vectors
- Integrity keys (Message Authentication)
Essentially everything in a cipher suite, and any (or all) can be renegotiated and changed when a Change Cipher Spec message is received.