In the context of a network, topology refers to the way the nodes of the network connect to each other.
A bus topology has all nodes connected to the same link. The advantage of this approach is in its simplicity and cost. Contention on the link requires either control signals to arbitrate between nodes wishing to use the link at the same time, or a means of detecting (and correcting) the situation when multiple nodes attempt to transmit data on the link simultaneously (called a collision). Ethernet networks use a bus topology that detects collisions and retransmits data afterwards.
A ring topology connects nodes in a circular arrangement which requires data destined for a given node to be passed through each node between the sender and destination. The data transmission may be mono- or bi-directional. Token Ring networks use a ring topology and pass data (called tokens) between the nodes to indicate which node is free to transmit data. After data is transmitted, the token is released.
A line topology resembles a ring topology, except that the ends of the line do not connect. Like a ring topology, data has to pass through each node between the sender and destination.
A star topology has a central node which is responsible for routing all network traffic between the rest of the nodes. The rest of the nodes connect only to the central node. The advantage is that there is no contention on the links, but on a busy network the central node will struggle to all of the traffic. The central node has a limited throughput, so if the demand is too high, the central node will no longer be able to manage the volume of traffic.
Wireless internet (WiFi, WiMax, etc.) must utilize this network architecture, with the wireless access point being the central node. A collision avoidance system is used to ensure that only one client is transmitting at a time. This kind of topology also has several other uses. For example, a star network may be used to isolate untrusted clients from each other using separate lines directly from each one to the router, where port security prevents communication between them.
A mesh topology consists of links between only two nodes, but each node has dedicated links to multiple other nodes. In a full mesh, each node has a dedicated link to every other node, thus the number of links will climb exponentially with the number of nodes. This is the most expensive topology for a given number of nodes, but also has the highest bandwidth. In partial meshes, the nodes have links only to some of the other nodes. This provides a slightly less expensive network with lower, but still significant, bandwidth. A mesh with only two or three nodes is indistinguishable from a ring.
A tree topology is a multi-level star topology. That is, the central node of one star is a terminal node of another star. This can happen to any number of levels.
A mixed topology contains more than one type of topology connected together. For instance, a bus topology could be connected to a star topology through one of the nodes.