There's two things you might call speed: bandwidth and latency.
Latency is the duration of time needed for a signal at one node of the network to reach another node of the network. Processing time for the electronics to packetize the signal and place it on the wire often dominates the latency, but the physical medium does also affect it. As far as the physical medium is concerned latency is largely determined by the distance between the nodes (measured along the actual connecting cables between them), and the propagation velocity of the transmission lines.
The propagation velocity of the transmission lines is determined mainly by the dielectric material between the conductors. It is typically between 1/2 and 3/4 c.
Bandwidth (as used in the field of networking) is the channel capacity, or amount of data that can be delivered by the system in a given time. For example, "100 megabits per second". The physical bandwidth capability of a transmission network is determined by the Shannon-Hartley equation
\$ C = B \log_2\left(1+\frac{S}{N}\right)\$
C is the channel capacity, B is the analog bandwidth (in Hz) of the system, and \$S/N\$ is the signal to noise ratio (SNR) of the receiver.
The SNR term is generally determined by the receiver electronics, though losses in the transmission medium will reduce the S portion of SNR.
B is the term where the physical medium has the most effect. Most media can be characterized by a bandwidth-distance product. Meaning a certain medium can carry more bandwidth if the distance is shorter.
Many of the technological advances that increased the network bandwidth (C) were achieved by using coding to take advantage of SNR to deliver more bits through cables with the same analog bandwidth (B). This was a major driver of advances in telephone modem speeds from 1200 to 56k baud, for example. These codes provide both error correction (to deal with the occasional incorrectly received bit) and equalization (to maximize use of the analog bandwidth of the medium).
10 Gb/s ethernet transmission over twisted pair is achieved by using 4 physical transmission lines per link, and by keeping the distance short (15 m), as well as by appropriate coding techniques.
