Although hardware protection of private or symmetric keys alone is a major improvement over software-generated keys, the TPM also offers strong access control. A software key often uses a password for access control, to protect the key. For example, the secret key may be encrypted with a password. This protection is only as strong as the password, and the secret key is vulnerable to an offline hammering attack. That is, once an attacker obtains the encrypted key, extracting the key is reduced to cracking the password. The key owner can't prevent a high-speed attack that tries an unlimited number of passwords. This attack can be parallelized, with many computers trying different passwords simultaneously. The cloud has made this kind of attack very feasible.
The TPM improves on software keys in two respects. First, when the key leaves the TPM (see the “Key Hierarchy” section), it's wrapped (encrypted) with a strong parent key encrypting key. The attacker now has to crack a strong key rather than a weak password.
Second, when a key is loaded in the TPM, it's protected by what the specification calls dictionary attack protection logic. Each time an attacker fails to crack the key's authorization,  this logic logs the failure. After a configurable number of failures, the TPM blocks further attempts for a configurable amount of time. This limits, possibly severely, the speed at which an attacker can try passwords. The rate limiting can make even a weak TPM key password much more time consuming to crack than a strong software key password, where the attack isn't rate limited. Chapter 13 describes password and HMAC authorization in detail.
The TPM provides many access-control mechanisms beyond a simple password.
However, it's the hardware protection of the dictionary-attack protection logic that makes a TPM key password resistant to attack.
Sometimes a key should be destroyed. Perhaps the authorization has been exposed. Perhaps the machine is being repurposed. Keys that are stored in software can never be destroyed, because they may have been copied almost anywhere. But TPM keys have parents or are primary keys.
As described in Chapter 9, there are three persistent hierarchies (endorsement, storage, and platform) plus one volatile hierarchy (the null hierarchy). Each hierarchy has its unique primary seed. Erasing a primary seed prevents re-creation of primary keys in that hierarchy—obviously a drastic and rarely performed action. Erasing the primary keys then prevents their children from being loaded in the TPM. Any key with attributes that prove it can only exist in the TPM is then destroyed.
-  Chapters 13 and 14 discuss the details of TPM authorization.