Remote vulnerability is a condition where the attacker has no prior access, but the vulnerability can still be exploited by triggering the malicious piece of code over the network. This type of vulnerability allows an attacker to gain remote access to a computer without facing any physical or local barriers.
For instance, Bob and Alice are individually connected to the internet. Both of them have different IP addresses, and are geographically dispersed in two different regions. Let's assume that Alice's computer is running on a Windows XP operating system and holds secret biotech information. We also assume that Bob already knows the operating system and IP address of Alice's machine. Bob now looks for a solution that can allow him to gain remote access to her computer. In time, he finds out that the MS08-067 Windows Server Service's vulnerability can easily be exploited remotely against a Windows XP machine.
He then triggers the exploit against Alice's computer and gains full access to it.