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I am moving my company to a leased line and in their brochure they have mentioned that I will be getting a /29 IPs. When I wanted to lookup how many IP addresses that will be, this page http://www.aelius.com/njh/subnet_sheet.html , I found this line:

    Addresses   Hosts   Netmask         Amount of a Class C
/30     4       2       255.255.255.252     1/64
/29     8       6       255.255.255.248     1/32

While I understand how I get 8 addresses, (since a /29 means 3-bits for addresses, given me 2^3 = 8 addresses), I don't understand what does "6 Hosts" mean? What is the differentiation between a host and an address in this case? How does it affect me?

Also, if someone could clarify what "Amount of a class C" means. I am thinking it means the ratio of addresses in a particular subnet to the total addresses in a class C network. Is this right?

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Like you said, a /29 leaves 3 bits for addresses. However, the first address is the network address and cannot be used for a host. Likewise, the last address is the broadcast address and also cannot be used.

Regarding your class C question, see https://en.wikipedia.org/wiki/Classful_network. However, the class A, B, and C terms are often used incorrectly to denote /8, /16, and /24, respectively. More than likely, that's what is meant when they are referring to the "amount of a class C". They are referring to a /24, which has 256 addresses - 254 which are usable for hosts.

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