Tier 1 network terms is usually used when we talk about computer networking, from meriam webster dictionary the definition of tier is :
a : a row, rank, or layer of articles; especially : one of two or more rows, levels, or ranks arranged one above another
b : a group of political or geographic divisions that form a row across the map (the southern tier of states)

this is taken from http://www.merriam-webster.com/dictionary/tier

Tier 1 network can be understood as rank 1 network, Tier 1 ISP then refers to Rank 1 ISP. from wikipedia the tier 1 network is an internet protocol network that participate in the internet via settlement-free interconnection called settlement free peering.

Tier 2 network / ISP is network that still needs tier 1 ISP reach some portion of (global) internet. This tier 2 ISP pays for unequal traffic flows between them, the term fee-based peering or transit is usually used to refers to this kind of settlement. Tier 2 network may connected through same size network with settlement free peering (tier 2 to tier 2)

While Tier 3 network / ISP is network that is connected to global internet through Tier 2 ISP. as the customer of bigger ISP, they pay for the transit fee to its Tier 1 or Tier 2 ISP.

You can observe the network hierarki from this image

Network Provider Hierarchy

From IDC White Paper (Tier 1 ISPs : What Are They And Why They Are Important) there are some characteristics that represent Tier 1 Network :

1. Tier 1 Networks Dont Pay for the trafic between similiar size networks
2. Tier 1 Networks Have access to all routing tables from their peering networks
3. Tier 1 Networks peer on one or more continent
4. Tier 1 Networks own or lease transoceanic fiberoptic transport
5. Tier 1 Networks deliver packet to and from customer and to and from peers around the world

Peering

in computer networks, peering means voluntary interconnection between separately internet network in purpose for exchange traffic between the customer of each network. Each participant doesn’t pay for the traffic, instead they get the money from their own customer. The term peering is used when two participant shared the same link with same size (equivalent sized partner).

The biggest internet provider that connected accross continent is example of tier 1 ISP. some of them will have underground oceanic backbone to ensure it can deliver the highest data rate.

There are 3 basic form of interconnection rules : public peering, private peering, and transit.

private peering refers to direct interconnection between two ISP. this connection is built via layer 1 and layer 2 link between ISP with similar networks capacity and traffic level. Its exclusive and expensive

public peering refers to multiple interconnection of network through internet exchange. it is the predominant model for exchanging traffic between ISP. The term public implies that many tier 1 or tier 2 networks can connect through it. The service itself can be free and commercial. the commercial one tough, tries to give the experience equal with private peering, they move incredible amount of traffic, without loss.

Transit refers to selling dedicated access through ISP network via private lease-line telecommunications circuits. Transit cost comes from circuit cost and variable cost associated with the traffic carried upstream to the internet.

You can read more about it here