Ethereum is a decentralized platform that runs smart contracts: applications that run exactly as programmed without any possibility of fraud or third party interference. In the Ethereum protocol and blockchain there is a price for each operation.
The general idea is, in order to have things run on the network you need to be rewarded with Ether (ETH), which is the crypto currency that fuels the network. People all over the world use ETH to make payments, as a store of value, or as collateral.
The way Ethereum makes sure there is only one blockchains is by using what is called a Proof of Work (PoW) algorithm. Ethereum miners are rewarded based on their share of work done, rather than their share of the total number of blocks mined.
This system was designed to make it difficult for someone to control the network by creating a large number of blocks, and then refusing to mine any more blocks. If this happened, the honest miners would be forced to mine on an empty blockchain while the attacker enjoyed all the rewards.
The PoW algorithm used by Ethereum, Ethash, is designed to be ASIC-resistant, meaning that it cannot be efficiently mined by special purpose hardware. This is intended to make it accessible to as many people as possible, and to prevent centralization of power among a small number of miners.
However, this does not mean that it cannot be mined at all with special purpose hardware; it just means that it will not be profitable to do so.
GPUs are well suited to mining Ethereum because they have lots of processing power and can do the repetitive work required by the PoW algorithm quickly and easily. However, they are not very efficient at doing so; a typical GPU will use more than 200 watts of electricity to mine 1 ETH per day.
This means that mining with a GPU is only profitable if you have very low electricity costs or you can sell your excess heat for some other purpose.
ASICs are specialized hardware that can mine much faster and more efficiently than GPUs, but they are expensive and difficult to obtain. ASICs are only manufactured by a few companies and they are not available for purchase by individuals.
ASICs are also centralized, which goes against the decentralizing philosophy of Ethereum.
It is possible to mine Ethereum with 4 GB GPU, but it is not profitable because GPUs are not very efficient at mining ETH and electric costs will eat into any profits made. ASICs are more efficient but they are expensive and centralized, so they are not ideal for mining ETH either.
The best way to mine ETH profitably is by joining a mining pool and sharing your rewards with other miners.