I'm about to purchase tablet computer. My main purpose will be to browse Internet. So, please tell whether the processor speed has to do anything with the Internet speed. Different tablets have different processor speed like 1GH, 1.2GH, 1.3GH, 1.6GH etc.
Does Internet speed depends on processor
Without a setup (bonding) from the access provider side, you cannot increase speed this way. It can increase volume (if doing two things at once, or running a network with multiple users through a router which has two uplinks, dividing user traffic between them) but a single connection is limited to going over a single link at the speed of that link - if there's only one connection, the other link will sit idle. The common method for doing so is to use a dedicated (PC-based) router machine which supports two uplinks - it must be possible to pull this off on a non-router machine, but it would be a headache compared to using an easily configured router (given that you are contemplating having the ready cash to throw at an extra internet connection.)
There is multiple reasons why your approach is flawed.
First - your bandwidth is limited by the connection of your internet uplink. Doubling the bandwidth of your computer improves the connection to your router - but that's about it. Your router can still only use the bandwidth of your uplink. And that is usually less than even the bandwidth of a single network card. Of course you can use two network cards connected to different routers on different uplinks (say, one fiber conneciton and one 4G wireless connection). But then, the other problem is still there.
Second - IP connections are stateful. A communicaiton is between two IP addresses. One source, and one destination. YOu cannot establish a connection with one IP address, and expect to receive data on another. Sure, you can forge IP packages and pretend they're coming from the other card, or half of them were coming from the other card, but even if you do that you can't expect any entity on the other end of the connection to know that it should treat all those packages as coming from the same source.
What you CAN do is tell your OS to route some routes over one network card, and others over the other. If both are connected to different uplinks, you can theorectically use the bandwidth of both uplinks at the same time - but only on parallel connections to different sources.
Internet's speed is the rate at which you can transfer data over the Internet. As Jonas Wielicki wrote in his answer, this should not be affected by CPU speed, at least not in a noticeable way.
User experience will be affected, though, because when browsing World Wide Web (which are not the same as the Internet - the former means websites, the latter is a global network used to transmit those, but also to send any other data - file transfers, Skype calls etc.) actual display times are more important than download speed.
Fast Internet connections (either over Wi-Fi or cellular connections) are widely available today and download speeds for most sites aren't that important. Here's a screenshot from Chrome's profiler showing load time breakdown for SuperUser on my current hardware and connection:
As you can see, loading takes only 67 milliseconds, while rendering, painting, running scripts and mysterious other tasks add up to one second. Downloading makes only a fraction of entire load time, as clearly visible on the pie chart. Other steps of displaying a website heavily depend on hardware, so CPU will matter when browsing.
So hardware is important if you're going to use that device for browsing WWW. There is no mobile CPU that will be definitely "fast enough". The higher the frequency is, the better it will perform. Number of cores also matters. Other factors may limit the CPU, like amount of RAM, its speed, storage memory's speed, operating system version and modifications applied by manufacturer.