SSL Certificate framework 101: How does the browser actually verify the validity of a given server certificate?

You are correct that SSL uses an asymmetric key pair. One public and one private key is generated which also known as public key infrastructure (PKI). The public key is what is distributed to the world, and is used to encrypt the data. Only the private key can actually decrypt the data though. Here is an example:

Say we both go to walmart.com and buy stuff. Each of us get a copy of Walmart's public key to sign our transaction with. Once the transaction is signed by Walmart's public key, only Walmart's private key can decrypt the transaction. If I use my copy of Walmart's public key, it will not decrypt your transaction. Walmart must keep their private key very private and secure, else anyone who gets it can decrypt transactions to Walmart. This is why the DigiNotar breach was such a big deal

Now that you get the idea of the private and public key pairs, it's important to know who actually issues the cert and why certs are trusted. I'm oversimplifying this, but there are specific root certificate authorities (CA) such as Verisign who sign certs, but also sign for intermediary CA's. This follows what is called Chain of Trust, which is a chain of systems that trust each other. See the image linked below to get a better idea (note the root CA is at the bottom).

Organizations often purchase either wildcard certs or get registered as a intermediate CA themselves who is authorized to sign for their domain alone. This prevents Google from signing certs for Microsoft.

Because of this chain of trust, a certificate can be verified all the way to the root CA. To show this, DigiCert (and many others) have tools to verify this trust. DigiCert's tool is linked here. I did a validation on gmail.com and when you scroll down it shows this:

This shows that the cert for gmail.com is issued by Google Internet Authority G2, who is in turn issued a cert from GeoTrust Global, who is in turn issued a cert from Equifax.

Now when you go to gmail.com, your browser doesn't just get a blob of a hash and goes on it's way. No, it gets a whole host of details along with the cert:

These details are what your browser uses to help identify the validity of the cert. For example, if the expiration date has passed, your browser will throw a cert error. If all the basic details of the cert check out, it will verify all the way to the root CA, that the cert is valid.

Now that you have a better idea as to the cert details, this expanded image similar to the first one above will hopefully make more sense:

This is why your browser can verify one cert against the next, all the way to the root CA, which your browser inherently trusts.

Hope this helps you understand a bit better!

To clarify one point from the question not covered in the otherwise excellent answer by @PTW-105 (and asked in the comment there by @JVE999):

I thought public key is to encrypt data, not to decrypt data...

The keys work both ways - what is encrypted with the public key can only be decrypted with the private and vice versa. We just decide one is private and one is public, there's no conceptual difference.

So if I encrypt data to send to you I use your public key to encrypt it and only you can decrypt it with your private key.

However, if I want to sign something, to prove it came from me, then I generate a hash of the message and encrypt that hash with my private key. Then anyone can decrypt it with my public key and compare to the actual message hash, but they know that only I could have encrypted it, since only I have my private key. So they know the message hash hasn't changed since I signed it, and therefore that it came from me.

As per the comments, the above is not quite true. See the link from the comment by @dave_thompson_085. However, this isn't a "how to sign properly" tutorial, just clarifying the roles of private and public keys in encryption verses signing. The basic point in that regard is this:

• To encrypt data the external party uses a public key and only the private key holder can decrypt it.
• To sign, the private key holder uses a hash function and their private key (plus appropriate padding, etc.). The external party can then verify the signature using the public key. This ensures the message came from the private key holder (assuming no-one else has access to the private key).

Signing may sometimes (depending on the implementation) be done with the same key pair as encryption, just used the other way round, or it may use a distinct key pair (see another link, also from @dave_thompson_085's comment)