A TCP/IP stack is a piece of software which connects your computer to the internet (or a LAN or whatever) using the TCP/IP protocol. A TCP/IP stack can do this through a lot of devices (typically a modem or a network card). The most advanced Amiga TCP/IP stack is called MiamiDeluxe, unfortunately that is no longer available. The other main contender is Genesis, but that doesn't support DHCP (or does it nowadays?, DHCP can be important in LANs or with broadband connections).
Genesis is included with OS 3.9. The new OS4 is supposed to have a brand new advanced TCP/IP stack called Roadshow. And all Amiga browsers are very outdated, but IB2.3 has the most features. (IIRC it doesn't support Shockwave Flash, whilst Voyager does).
Demo versions of Miami and Genesis can probably found on Aminet (probably with a 30 minute timeout).