What is Hive Engine?
So hive-engine.com is the first practical HIVE-based attempt at a token economy and smart-contract environment for HIVE via a side-chain platform. Although not directly connected to HIVE, it integrated into it to the extent that its difficult to imagine HIVE without it. It originated from an earlier implementation found steem-engine.net for the STEEM blockchain, but was reimagined and reconstituted for the HIVE blockchain after the community exodus from STEEM.
This introduced the concept of non-fungible tokens (NFTs) to HIVE, where users like you and me could create our own HIVE-based tokens. The same could apply to whole communities (known as tribes on HIVE). Through a service known as Nitrous, tribes could now implement their own customized version of the web interface for the blockchain. Likewise through a service known as Scotbot, such tribes could implement their own token environment, including programming how distribution was carried out (akin to how hive inflation is rewarded). Essentially these two services helped tp create HIVE-based sidechain clones of STEEM/HIVE that complemented HIVE.
Instead of only being rewarded in STEEM/HIVE, one could also be rewarded in custom tokens as well. For example, if I did a single upvote of a post tagged with the "leofinance" tag, this would calculate separately the share of HIVE rewards (out of the inflation pool) I could attribute via my HIVE POWER but it would also reward LEO respectively via the amount of LEO POWER I had.
It is for this reason many people would begin to create separate accounts specifically to hold the hive engine tokens. Instead of 
Every token has its own market and all of them are traded against HIVE in these markets for their trading pairs. Some tokens have the ability to be staked, some could operate with inflation, some where fungible, and some were non-fungible.
A game like Splinterlands.com for example can only work because of Hive-Engine, and its ability to mint millions of NFTs, each with unique attributes. One token could represent a uniquely identified card in the game from a distinct version of the card pack edition, with unique fighting capabilities, and unique levels of gameplay.
There are also things like miner tokens, where tokens could be programmed to give holders of these miner tokens a chance to earn some of the set inflation rate of another token. For example, the token LEOM is a mining token for LEO. By merely owning and staking LEOM, the stakeholder will earn some LEO tokens over time. Yes, instead of buying capital-intensive mining rigs for something like Bitcoin and spending intense energy costs, one could "mine" by owning and staking tokens.
Tokens could be sent and delegated just like HIVE. Integrated into Hive Keychain, one can easily send tokens via this chrome extension method as well.